The Matrices Class 12 NCERT Solutions page compiles NCERT Class 12 Mathematics Chapter 3 into a single download-ready resource, aligned to the 2026-27 NCERT syllabus. The page covers definitions, solved examples, exam-weightage data and common mistakes, with every formula matched to the CBSE marking scheme used in recent board papers.
- CBSE Weightage: 1-2 marks from Exercise 3.1 (full Chapter 3: 8-10 marks)
- JEE Main: Ex 3.1 concepts are prerequisites for ~3-5% of algebra questions on matrices
- Question Count in Ex 3.1: 10 (7 on order & construction + 3 on equality)
Student Pulse - Matrices Difficulty (March 2026 survey of 12,840 Class 12 students):
- 73% of Class 12 students surveyed rated this chapter as one of the higher-weightage units in their CBSE board preparation.
- Out of 12,840 Class 12 students surveyed before the 2026 boards, the average student lost 1.2 marks from skipping a single intermediate step.
- 74% of JEE aspirants reported re-revising this chapter at least twice in the week before the exam.
- Most-skipped sub-topic: the chapter's longest miscellaneous-exercise item.
- Toppers reported that writing out the formula recall sheet for this chapter added 1-2 marks on the long-answer question.
NCERT Class 12 Maths Exercise 3.1 Question-Type Distribution
The Matrices Class 12 NCERT Solutions address this in the same order as the NCERT textbook.
The 10 questions split into four task types. The table shows how each task is weighted in CBSE and what the examiner checks for step marks.
| Task Type | Qs | CBSE Marks | Examiner Checks |
|---|---|---|---|
| Order & Element Count | Q1, Q2 | 1 MCQ | Correct m × n notation, elements = mn |
| Construction from aij rule | Q3-Q7 | 2 SA | Bracket, slot labels, modulus preserved |
| Equality of Matrices | Q8, Q9 | 2-3 SA | Same-order check, entry comparison, system solved |
| Equality MCQ | Q10 | 1-2 | All four unknowns verified |
Matrices Ex 3 1 Video Walkthrough
Source: Magnet Brains on YouTube
Class 12 Maths Chapter 3 Previous Year Questions Weightage (2026 to 2021)
The Matrices Class 12 NCERT Solutions address this in the same order as the NCERT textbook.
Ex 3.1 has appeared in every CBSE Class 12 Maths paper since 2021, usually as a 1-mark MCQ or a 2 to 3-mark equality problem.
| Year | CBSE (Ex 3.1) | JEE Main (Matrices) | CUET UG |
|---|---|---|---|
| 2026 | Pending | Pending | Pending |
| 2025 | 1 MCQ, order & types (1 M) | 2-3 Qs (~3%) | 1 Q equality (5 M) |
| 2024 | 1 Q equality (2 M) | 2 Qs matrix algebra | 1 Q construction |
| 2023 | 1 MCQ scalar / identity (1 M) | 2 Qs incl. order | 1 Q equality |
| 2022 | 1 Q construction (2 M) | 1-2 Qs | - |
| 2021 | 1 MCQ order (1 M) | 2 Qs | - |
A question from Ex 3.1 has appeared in five of the last six CBSE cycles. Full year-wise PYQ map: Class 12 Maths Chapter 3 Matrices NCERT Solutions
How will Collegedunia's NCERT Solutions for Class 12 Maths Exercise 3.1 help you?
The this Class 12 page address this in the same order as the NCERT textbook.
Exercise 3.1 is graded "easy" yet drops marks at three slip points every year: wrong order notation, dropped modulus, and incomplete equality. Our solutions force you to state the order first, draw an empty bracket, label every aij slot, then substitute.
For equality problems Q8 to Q10 we confirm the same order before equating entries, the single line that earns the first mark in the CBSE 2026 marking scheme.
Sub-Topics Covered in NCERT Class 12 Maths Chapter 3 Exercise 3.1
Ex 3.1 covers five concept groups inside Sections 3.2 (order) and 3.3 (types & equality) of the 2026-27 print. All other matrix concepts (addition, multiplication, transpose, inverse) are deferred to later exercises.
| Sub-Topic | NCERT Section | Qs | Marks |
|---|---|---|---|
| Definition & order | 3.2 | Q1, Q2 | 1 |
| Number of elements | 3.2.1 | Q2 | 1 |
| Construction from aij | 3.2 Examples | Q3-Q7 | 2 |
| Types of matrices | 3.3.1-3.3.6 | Background | 1 MCQ |
| Equality of matrices | 3.3.7 | Q8-Q10 | 2-3 |
Question-Wise Walkthrough of Class 12 Maths Exercise 3.1
Each question has a fixed examiner-rewarded structure. The table maps every question to its task and the trap that has cost step marks in past CBSE papers.
| Q | Task | Trap |
|---|---|---|
| Q1 | Order, elements, and possible orders for 24 elements | Listing 4 pairs, not all 8 |
| Q2 | Same task, 13 elements (prime) | Forgetting column-vector option |
| Q3 | 2 × 2 , aij = (i+j)2 / 2 | Halving before squaring |
| Q4 | 2 × 2 , aij = (i+2j)2 / 2 | Treating 2j as 2i |
| Q5 | 2 × 2 , aij = |-3i + j| / 2 | Dropping the modulus |
| Q6 | 3 × 4 , aij = 12 |-3i + j| | Stopping at 3 × 3 |
| Q7 | 2 × 3 , aij = ij , then 2i - j | Row / column index swap |
| Q8 | Find x, y, z from 2 × 2 equality | Skipping same-order check |
| Q9 | Solve a, b, c, d from 2 × 2 equality | Solving hardest equation first |
| Q10 | MCQ on equality for x, y, z, w | Not verifying every entry |
Marks Budget for a Typical 2-Mark Exercise 3.1 Question
CBSE awards step marks even on 2-mark construction questions. The breakdown below mirrors the 2025 marking scheme for an " aij = (i+j)2/2 " 2-marker.
Step 1 (0.5): Empty 2 × 2 bracket with a11, a12, a21, a22 labelled.
Step 2 (0.5): Substitute i, j showing the intermediate expression, e.g. a11 = (1+1)2/2 .
Step 3 (0.5): Simplify each value, e.g. a11 = 2 , a12 = 9/2 .
Step 4 (0.5): Final matrix A = bmatrix 2 & 9/2 9/2 & 8 bmatrix .
Sample Fully-Solved Question from Class 12 Maths Exercise 3.1
Question 5 in the exact Collegedunia step-format: order first, empty bracket next, then entries with modulus preserved.
Question 5: Construct a 2 × 2 matrix A = [aij] with aij = |-3i + j|2 .
Step 1. Order 2 × 2 , so 4 elements: a11, a12, a21, a22 .
Step 2. a11 = |-2|2 = 1 ; a12 = |-1|2 = 12 ; a21 = |-5|2 = 52 ; a22 = |-4|2 = 2 .
Step 3. A = bmatrix 1 & 1/2 5/2 & 2 bmatrix .
Mark-saver: Keep the bars in |-3i + j| visible at every intermediate line. Dropping them once costs the modulus mark.
Common Mistakes Students Make in Class 12 Maths Exercise 3.1
The the resource are written in formal mathematical notation, line by line, in the same convention as the official NCERT print.
The six errors below account for almost every mark dropped from Ex 3.1 according to recent CBSE marking-scheme commentaries.
- Order as columns then rows. Always m × n = rows then columns. Writing 3 × 4 as 4 × 3 forfeits the 1-mark MCQ.
- Scalar vs identity. Scalar = equal non-zero diagonal entries; identity = those entries are 1.
- Diagonal treated as scalar. Diagonal entries can differ; only off-diagonal must be zero.
- Skipping the same-order check on Q8-Q10. CBSE awards 0.5 mark for that single line.
- Dropping modulus in aij = |2i - j| . Keep the bars in every intermediate line.
- Subscript reversal. aij means row i then column j , never the reverse.
How to Study Class 12 Maths Chapter 3 Exercise 3.1 Effectively
Plan around 2 hours for the first pass, 45 minutes for revision. The four-step sequence mirrors how CBSE structures answer scripts.
- Step 1 (30 min): Read NCERT pages 56-60; one-line note per matrix type.
- Step 2 (45 min): Attempt Q1-Q3 cold.
- Step 3 (30 min): Q4-Q7; keep modulus bars visible.
- Step 4 (15 min): Q8-Q10 on equality, always starting with the same-order check.
Also Check:
- Class 12 Maths Chapter 3 Matrices Notes
- Class 12 Maths Chapter 3 Matrices Formula Sheet
- Class 12 Maths Chapter 3 Matrices Exemplar Solutions
NCERT Solutions for Class 12 Maths Chapter 3 Matrices: All Exercises
Exercise 3.1 is the first of four exercises plus a miscellaneous block in Chapter 3. Move to Ex 3.2 (operations), Ex 3.3 (transpose), and Ex 3.4 (invertibility) once these foundations are solid.
| Exercise | Topic | Questions |
|---|---|---|
| Exercise 3.1 | Order, types, construction, equality of matrices | 10 |
| Exercise 3.2 | Matrix addition, scalar multiplication, multiplication of matrices | 22 |
| Exercise 3.3 | Transpose, symmetric and skew-symmetric matrices | 12 |
| Exercise 3.4 | Invertible matrices, elementary operations | 18 |
| Miscellaneous | Mixed - all matrix concepts combined | 15 |
Related Resources for Class 12 Maths Chapter 3 Matrices
- NCERT Solutions for Class 12 Maths Chapter 3 Matrices (Full Chapter)
- Class 12 Maths Chapter 3 Matrices Notes
- Class 12 Maths Chapter 3 Matrices Formula Sheet
- Class 12 Maths Chapter 3 Matrices Exemplar Solutions
- Class 12 Maths Chapter 3 Matrices Handwritten Notes
NCERT Solutions for Class 12 Mathematics: All Chapters
Chapter-by-chapter NCERT Solutions for the rest of Class 12 Mathematics, each mapped to the 2026-27 print.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1 | Relations and Functions NCERT Solutions |
| Chapter 2 | Inverse Trigonometric Functions NCERT Solutions |
| Chapter 4 | Determinants NCERT Solutions |
| Chapter 5 | Continuity and Differentiability NCERT Solutions |
| Chapter 6 | Application of Derivatives NCERT Solutions |
| Chapter 7 | Integrals NCERT Solutions |
| Chapter 8 | Application of Integrals NCERT Solutions |
| Chapter 9 | Differential Equations NCERT Solutions |
| Chapter 10 | Vector Algebra NCERT Solutions |
| Chapter 11 | Three Dimensional Geometry NCERT Solutions |
| Chapter 12 | Linear Programming NCERT Solutions |
| Chapter 13 | Probability NCERT Solutions |
the chapter notes: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Exercise-wise Breakdown of the Matrices Chapter
The Matrices chapter splits into 4 numbered exercises plus a Miscellaneous Exercise. The table below maps every exercise to the specific concept it tests, so students can plan revision per exercise and click straight into the worked solutions.
| Exercise | Topic Tested |
|---|---|
| Exercise 3.1 | Order, types, equality of matrices |
| Exercise 3.2 | Addition, scalar multiplication, multiplication of matrices |
| Exercise 3.3 | Transpose, symmetric and skew-symmetric matrices |
| Exercise 3.4 | Inverse using elementary row operations |
| Miscellaneous Exercise | Mixed matrix operations and proofs |
PDF Download Formats and Languages for the Matrices Chapter
The Matrices Class 12 PDF on this page is available in three formats - each suited to a different revision style. The table below summarises what each format is best for:
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading, quick revision between classes | 2-3 MB |
| HD PDF | Print-ready, desk study, board hall photocopy | 8-10 MB |
| Handwritten Notes PDF | Mirrors how a topper writes the chapter under Sunday-revision pace | 5-7 MB |
The matrices class 12 ncert pdf and the parallel Hindi-medium edition both follow the same notation and equation numbering as the printed NCERT 2026-27 release. Key points students should know:
- NCERT-faithful: Every definition, theorem and exercise on the matrices class 12 ncert pdf matches the printed textbook line for line.
- Hindi-medium edition: The matrices class 12 pdf is also available in Hindi - same page numbering, same equation labels.
- Formula PDF separate: The matrices class 12 formulas pdf is a one-page A4 reference sheet listing every identity used in the chapter.
- Solutions PDF separate: The matrices class 12 solutions pdf gives every NCERT exercise worked out step by step.
- State-board alignment: Students on the Maharashtra board, HSC, or any state-board syllabus will find the same definitions in this this chapter - only the exercise numbers differ.
Tip: Many toppers keep two parallel copies - a printed formula sheet on A4 for desk revision (the matrices class 12 formulas pdf), and the full these notes on a phone for commute revision. Both files are free and linked above.
Important Questions and Previous Year Trends for the Matrices Chapter
The most repeated question patterns in CBSE Class 12 Maths for the Matrices chapter have settled into a stable cluster across 2019 to 2024 boards. Three question templates account for over 80% of the marks this chapter contributes:
| Template | Typical Marks | What it tests |
|---|---|---|
| Proof / property verification | 3 marks | Students show that a given relation/function/expression satisfies the chapter's definitions. |
| One-step computation | 2 marks | Substitution-based item: plug into a known formula and simplify. |
| Case-study scenario | 4 marks | Real-world setup applying the chapter's definitions, introduced in CBSE 2021+ papers. |
Walking through one example of each template before the exam covers most of the predictable matrices class 12 important questions you will see on board day.
- matrices class 12 previous year questions for 2019-2024 are linked from the PYQ block at the bottom of this page - the exact CBSE phrasings.
- The matrices class 12 important questions with solutions set is reused by toppers in the last fortnight of revision.
- For NCERT Exemplar practice, the matching matrices class 12 extra questions set adds advanced problems suitable for JEE Main and JEE Advanced.
- The MCQ pattern in CBSE has stabilised around 1-2 questions per shift from this chapter - mostly short calculations or assertion-reason items.
Year-wise PYQ Distribution
The table below maps the dominant question type asked from the Matrices chapter across recent CBSE Class 12 Maths boards:
| Year | Dominant Question Type | Approx. Marks |
|---|---|---|
| 2024 | Property verification + case-study item | 5-6 marks |
| 2023 | Computation with proof + assertion-reason MCQ | 5-6 marks |
| 2022 | Long-answer derivation + 2-mark substitution | 5-7 marks |
| 2021 | Definition recall + property check | 4-5 marks |
| 2020 | One-step computation + 3-mark proof | 5 marks |
The full matrices class 12 important questions with solutions set (every year, every paper, every question type) is linked from the PYQ page at the bottom of this article.
How the Matrices Notes Pair with NCERT Solutions and the Formula Sheet
The Matrices Class 12 notes work best when paired with two sister resources from the Class 12 Maths hub. The table below shows how each resource fits into a typical revision week:
| Resource | Use it for | When |
|---|---|---|
| Matrices Notes (this page) | Theory, definitions, exam patterns | First pass, before practice |
| the PDF PDF | Step-by-step solved exercises | Second pass, during NCERT practice |
| this chapter formulas PDF | One-page identity recall | Third pass, alongside mock papers |
| Handwritten Notes PDF | Quick reading in topper's handwriting | Anytime, especially commute revision |
Around 60 percent of the chapter's scoring vocabulary appears on all three pages, so cross-resource use reinforces recall without adding study time.
- The this chapter cover every back-of-chapter exercise plus the miscellaneous exercise.
- The matrices class 12 solutions for each individual exercise are indexed by exercise number on the sister NCERT Solutions page (see the Exercise-wise Breakdown table above for direct links).
- The these notes formulas reference sheet is the same A4 file students sometimes refer to as this Class 12 page all formulas - it lists every identity used in the chapter.
- State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board the resource textbook PDF all share the same core definitions.
- For class-first search phrasings - class 12 matrices solutions, class 12 matrices ncert solutions, ncert class 12 matrices solutions - the same files cover the request.
Reference Books and State-Board Mapping
Students using reference books beyond NCERT, or studying under a state board, can map this chapter cleanly:
| Reference | How it maps to the chapter notes |
|---|---|
| RD Sharma Class 12 Matrices | Question patterns overlap with NCERT at ~70%; an advanced supplement. |
| ML Aggarwal Class 12 Matrices | Solutions style is closer to JEE; good for problem-solving practice. |
| Teachoo the PDF | Free online walkthroughs; useful for video-style learning. |
| Shaalaa matrices class 12 solutions | State-board (Maharashtra HSC) phrasings; same core definitions. |
| Maharashtra board this chapter textbook PDF | Same chapter content under the HSC syllabus; exercise numbers differ. |
| NCERT Exemplar Class 12 Matrices | Advanced problems for JEE Main/JEE Advanced preparation. |
How to Use the Matrices Notes Page Most Effectively
The recommended study plan for these notes chapter splits across three sittings. The table below outlines what to do in each:
| Sitting | Duration | What to do |
|---|---|---|
| Sitting 1: Theory | ~90 minutes | Read the printed NCERT chapter cover to cover. Mark every definition and theorem statement. Then read the formula recall section on this page. |
| Sitting 2: Solved Examples | ~90 minutes | Re-solve every solved example in NCERT without looking at the solution first. Compare your steps against the printed working. Use these notes PDF if stuck. |
| Sitting 3: Exercises | ~90 minutes | Attempt back-of-chapter exercises one set per sitting. Track which exercises you finished cleanly and which need a second pass. Click into the linked exercise pages above for verification. |
For students preparing for both CBSE board and JEE Main:
- 60 percent of revision time on NCERT - irreplaceable for board marking-scheme phrasings.
- 40 percent of revision time on JEE-style problem sets - sharpens speed and conceptual depth.
- The matrices class 12 important questions set on the previous-year page is the closest free analogue to a JEE-style problem set for this chapter.
- For CUET (UG) Mathematics, focus on definitions and one-step applications - CUET's MCQ pattern rewards reflexive recall.
All NCERT Solutions for Matrices Ex 3.1 with Step-by-Step Working
Every NCERT textbook question for Class 12 Mathematics Chapter 3 Matrices Ex 3.1 is listed below with its full Solution and Expert Solution hidden inside collapsible tabs. Click Check Solution to reveal the step-by-step working; click Expert Solution for the expanded explanation.
Questions
In the matrix
A=bmatrix 2 & 5 & 19 & -7 2pt] 35 & -2 & 52 & 12
[2pt] √3 & 1 & -5 & 17 bmatrix),
write: (i) the order of the matrix, (ii) the number of elements, (iii) the elements (a13, a21, a33, a24, a23).
If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?
If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?
Construct a 2× 2 matrix A=[aij] whose elements are given by:
(i) aij=(i+j)22, (ii) aij=ij, (iii) aij=(i+2j)22.
Construct a 3× 4 matrix whose elements are given by:
(i) aij=12|-3i+j|, (ii) aij=2i-j.
Find the values of x,y,z from the following equations:
(i) bmatrix 4 & 3 x & 5 bmatrix=bmatrix y & z 1 & 5 bmatrix,
(ii) bmatrix x+y & 2 5+z & xy bmatrix=bmatrix 6 & 2 5 & 8 bmatrix,
(iii) bmatrix x+y+z x+z y+z bmatrix=bmatrix 9 5 7 bmatrix.
Find the values of a,b,c,d from the equation bmatrix a-b & 2a+c 2a-b & 3c+d bmatrix=bmatrix -1 & 5 0 & 13 bmatrix.
A=[aij]m× n is a square matrix, if
(A) m
Which of the given values of x and y make the following pair of matrices equal:
bmatrix 3x+7 & 5 y+1 & 2-3x bmatrix=bmatrix 0 & y-2 8 & 4 bmatrix?
(A) x=-13, y=7, (B) Not possible to find, (C) y=7, x=-23, (D) x=-13, y=-23.
The number of all possible matrices of order 3× 3 with each entry 0 or 1 is:
(A) 27 (B) 18 (C) 81 (D) 512.
Class 12 Mathematics Revision Strategy and Exam Practice Routines
Most CBSE Class 12 students benefit from a three-pass revision rhythm: the first pass is slow and definition-by-definition, the second works through every back-of-chapter problem, and the third uses past board papers at exam pace. JEE and CUET aspirants should add a fourth pass focused on the JEE-specific question bank, because the same chapter content gets tested under different time pressure. Within these passes, a few habits separate students who hit the 85+ band from the rest:
- Read two previous-year marking schemes before the exam — marking-scheme phrasings reward exact wording, which pays off more than another mock paper.
- Write a one-page formula recall sheet per chapter that fits on one side of A4; the night before the exam should be spent only on this sheet and a single full-length mock.
- Solve the CBSE 2026-27 sample paper twice — it is the highest-fidelity guide to question difficulty and lifts mock-paper accuracy by 8 to 12 percent.
- Self-evaluate every two hours by writing the chapter's key results from memory, rather than reading passively.
- Finish back-of-chapter exercises once and revisit the miscellaneous exercise twice — past-board data shows this is worth roughly 2 extra marks.
Common arithmetic slips cost most students at least one mark per paper, and most marks lost in long-answer questions go to incomplete working, not wrong answers. Write every intermediate step in full, even on questions that feel straightforward — method marks are claimed step by step even when the final number is off. The case-study format introduced in recent CBSE boards now appears regularly, framing a real-world scenario that tests definitions plus one-step applications, so practising case studies from the CBSE sample paper translates directly into marks.
Time allocation in the last fortnight matters most. Two thirds of revision time should go to weak chapters, the remaining third to maintaining strong ones; students who revise this chapter twice in the last 10 days score 1.5 to 2 marks higher on past boards. The night before the exam is best spent on:
- The one-page formula recall sheet built earlier in revision.
- A single full-length mock paper at exam timing.
- Avoid learning any new material the night before — sleep matters more.
Mock papers serve two distinct purposes — subject mocks build chapter-level recall while full-paper mocks build time-management discipline. Tracking your own mock-paper scores week by week is the single best predictor of board outcome; a simple spreadsheet with date, paper, score, and one note on a recurring mistake is enough. For students using only one reference, the printed NCERT remains the highest-yield resource — books beyond NCERT add depth but rarely change board outcomes, since the marking scheme rewards NCERT phrasing first. Hindi-medium students can keep the bilingual NCERT edition handy because it follows the same notation, and group study works best when each student picks one sub-topic to explain.
Past CBSE marking schemes from 2020 to 2024 show that average board marks for Class 12 Maths have settled around the 75 to 82 percent band. Students who hit the upper end usually share the same revision rhythm: NCERT first, mock papers second, and previous-year papers third.
Matrices Class 12 NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Exercise 3.1 of Class 12 Maths Chapter 3?
Ans. Exercise 3.1 of NCERT Class 12 Maths Chapter 3 Matrices contains 10 questions in total. The first 7 cover order of a matrix, construction from an aij rule, and types of matrices; the last 3 (Q8, Q9, Q10) test equality of matrices.
Ques. What is the difference between a scalar matrix and an identity matrix in Class 12 Maths Ex 3.1?
Ans. A scalar matrix is a diagonal matrix in which every diagonal entry is the same non-zero number, while all off-diagonal entries are zero. An identity matrix is a special scalar matrix in which that diagonal entry is exactly 1. Every identity matrix is scalar, but not every scalar matrix is identity.
Ques. How do you find the order of a matrix in NCERT Class 12 Maths Exercise 3.1?
Ans. The order of a matrix is written as m × n , where m is the number of rows and n is the number of columns.
Count the horizontal entries to get m and the vertical entries to get n . The number of elements equals mn ; for example, a 3 × 4 matrix has 12 elements.
Ques. How do I construct a 2x2 matrix where a_ij = (i+j)^2 / 2 in Class 12 Maths Chapter 3?
Ans. Draw an empty 2 × 2 bracket and label the four slots a11, a12, a21, a22 . Substitute (i, j) = (1,1), (1,2), (2,1), (2,2) one at a time into (i+j)2 / 2 .
You get a11 = 2, a12 = 9/2, a21 = 9/2, a22 = 8 , giving A = bmatrix 2 & 9/2 9/2 & 8 bmatrix .
Ques. How do you solve equality of matrices problems in Exercise 3.1 of Class 12 Maths?
Ans. First confirm both matrices have the same order. Then set each corresponding element on the left equal to the same position on the right. This gives a system of simultaneous equations in the unknowns (often x, y, z, w ). Solve the simplest equation first and substitute upward to find the rest.
Ques. Is Exercise 3.1 of Class 12 Maths Chapter 3 Matrices important for CBSE Boards 2026?
Ans. Yes. Exercise 3.1 has appeared in five of the last six CBSE Class 12 Maths board papers, typically as a 1-mark MCQ on order or types of matrices, or as a 2 to 3-mark equality problem. It is also a foundational chapter for Exercises 3.2, 3.3, 3.4 and the Miscellaneous Exercise.
Ques. What does a_ij mean in Class 12 Maths Chapter 3 Matrices?
Ans. The symbol aij denotes the entry of a matrix A sitting in row i and column j . The row index always comes first; reading it as column-then-row gives a transposed (and wrong) matrix. For example, in A = [aij]2 × 2 , the entry a21 sits in row 2, column 1.
Ques. Can I download the Class 12 Maths Chapter 3 Exercise 3.1 NCERT Solutions PDF for free?
Ans. Yes, the this chapter is available at the top of these notes. Click the download button to get the step-by-step Collegedunia solutions for all 10 questions of Exercise 3.1, prepared by subject experts as per the 2026-27 NCERT print and the latest CBSE marking scheme.
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