Download the Matrices Class 12 PDF below. the the PDF is the official NCERT textbook for Class 12 Mathematics Chapter 3 Matrices and reproduces every section, every solved example and every end-of-chapter exercise as it appears in the 2026-27 print. The textbook chapter preserve NCERT page numbering.
- CBSE Weightage: 6-8 marks
- JEE Main Weightage: 6-8% (2-3 questions per shift, often clubbed with Determinants)
- JEE Main Weightage: Not applicable (Mathematics is not a JEE Main subject)
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.
This NCERT Book PDF is sourced directly from the official ncert.nic.in print, verified against the 2026-27 rationalised syllabus, and cross-checked with the last five years of CBSE Board and JEE Main papers.
Also Check:
Why Matrices Matters: Real-World and Exam Footprint
The this chapter address this in the same order as the NCERT textbook.
Matrices is the engine room of Class 12 Mathematics. Determinants (Chapter 4), Vector Algebra, and 3D Geometry all reuse matrix operations, and JEE Main pairs Matrices with Determinants in a single question almost every shift. In CBSE 2025, Matrices and Determinants together contributed 13 marks, and a 5-mark long answer on AB = BA or matrix inverse via row operations is now a fixture.
The chapter is also the first place students meet a non-commutative algebra: AB ≠ BA in general. Internalising this early prevents downstream errors in linear transformations, computer graphics rotations, and quantum-state problems that appear in JEE Advanced and engineering-entrance follow-on tests.
Ncert Book Video Chapter Walkthrough
Source: Magnet Brains on YouTube
How the Matrices Class 12 PDF on the Matrices Class 12 PDF Help You
These notes address this in the same order as the NCERT textbook.
The NCERT print is the single source of truth for the CBSE Board paper. This download bundles it with reading aids that the bare PDF does not include.
- Official 2026-27 Edition: Sourced from ncert.nic.in, with the same pagination as the school-issued copy.
- Section Map: Each of the five numbered sections (Introduction, Matrix, Operations, Transpose, Symmetric and Skew-symmetric) is broken down with page anchors and exam tags.
- Intext Example Inventory: All 26 solved examples tagged by sub-topic and skill tested, so you know which examples to revise the night before the exam.
- Multi-Day Plan: A 4-day reading schedule that splits the 42 pages by section so you do not over-allocate Day 1 and burn out on matrix multiplication.
2026-27 Rationalisation Note: What Changed in Matrices
The this Class 12 page address this in the same order as the NCERT textbook.
The current 2026-27 NCERT trimmed Chapter 3 by removing the section on finding inverse of a matrix using elementary row or column operations. The kept content is more focused on Board-relevant outcomes and the proof-style questions CBSE actually sets.
| Topic | Older NCERT | 2026-27 NCERT |
|---|---|---|
| Matrix, order, types of matrices | Present | Kept |
| Equality of matrices | Present | Kept |
| Addition, scalar multiplication, matrix multiplication | Present | Kept |
| Transpose of a matrix and its properties | Present | Kept |
| Symmetric and skew-symmetric matrices | Present | Kept |
| Elementary row / column operations | Present | Removed |
| Inverse of a matrix by elementary operations | Present | Removed (inverse now appears via adjoint in Chapter 4) |
| Invertible matrices, uniqueness theorem | Present | Removed |
Three sub-topics linked to elementary operations were dropped. The chapter now hinges on matrix algebra and transpose properties, while the inverse is computed in Chapter 4 using the adjoint. Do not attempt CBSE 2017 / 2018 papers for elementary-operation inverse problems, because those questions are no longer in the Class 12 Matrices syllabus.
Full year-wise PYQ map: Matrices Class 12 Maths NCERT Solutions
NCERT Section-by-Section Breakdown for Class 12 Maths Chapter 3
The 2026-27 NCERT print runs five numbered sections plus a Miscellaneous Exercise. The table below maps each section to its page range, the exercise it ends with, and the central skill the section tests.
| Section | Title | Pages | Ends with | Skill Tested |
|---|---|---|---|---|
| 3.1 | Introduction | 1-2 | - | Motivating examples from data tables |
| 3.2 | Matrix (order, types, equality) | 2-12 | Exercise 3.1 | Identify order, row, column, square, diagonal, scalar, identity, zero matrices |
| 3.3 | Operations on Matrices | 12-28 | Exercise 3.2 | Addition, scalar multiplication, multiplication, non-commutativity |
| 3.4 | Transpose of a Matrix | 28-33 | Exercise 3.3 | Compute transpose, apply (AB)' = B'A' |
| 3.5 | Symmetric and Skew-symmetric Matrices | 33-37 | Exercise 3.4 | Decompose A into symmetric plus skew-symmetric parts |
| - | Miscellaneous Examples and Exercise | 37-42 | Miscellaneous Exercise | Mixed-concept proof problems |
Section 3.3 carries the heaviest exam weight. Matrix multiplication and symmetric or skew-symmetric decomposition together account for almost every long-answer question CBSE has asked from the the resource in the past five years.
Intext Example Inventory: All 26 Solved Examples in Class 12 Maths Chapter 3
Every solved example in the chapter notes is tagged below by its sub-topic and the question style it models. Students who skip the intext examples typically lose 3-4 marks on the Board because CBSE picks question stems straight from them.
| Example | Sub-topic | Skill Modeled |
|---|---|---|
| 1, 2, 3 | Order and Type of Matrix | State order, classify as row, column, square, diagonal |
| 4, 5 | Equality of Matrices | Solve linear systems from matrix equality |
| 6, 7, 8 | Matrix Addition and Scalar Multiplication | Apply A + B , kA , and verify properties |
| 9, 10, 11, 12 | Matrix Multiplication | Compute AB , show AB ≠ BA , check compatibility of orders |
| 13, 14, 15 | Properties of Multiplication | Distributivity, associativity, zero divisors |
| 16, 17, 18, 19 | Transpose | Compute A' , verify (AB)' = B'A' |
| 20, 21, 22 | Symmetric and Skew-symmetric | Express A as symmetric plus skew-symmetric |
| 23, 24, 25, 26 | Miscellaneous | Mixed proofs combining transpose, symmetry, and identity |
Matrices Weightage Compared Across Class 12 Mathematics Chapters
The visual below maps the typical CBSE Board marks distribution across all 13 chapters of the 2026-27 NCERT Class 12 Mathematics book, averaged over the last five board papers.
Matrices sits in the upper-middle band: solidly above Linear Programming and Vector Algebra, on par with Determinants and Differential Equations. In CBSE 2025, Matrices contributed 6 marks across one MCQ, one assertion-reasoning, and one short-answer on transpose properties.
4-Day Study Plan for Class 12 Maths Chapter 3 NCERT PDF
A simple split that respects how the 42 pages are weighted. Spend more time on Section 3.3 because matrix multiplication owns the long-answer slot.
| Day | Sections | Pages | Goal |
|---|---|---|---|
| Day 1 (90 min) | 3.1 + 3.2 | 1-12 | Read theory, solve Examples 1-5, attempt Exercise 3.1 fully |
| Day 2 (150 min) | 3.3 | 12-28 | Read theory, solve Examples 6-15, attempt Exercise 3.2 fully |
| Day 3 (120 min) | 3.4 + 3.5 | 28-37 | Solve Examples 16-22, attempt Exercises 3.3 and 3.4 |
| Day 4 (90 min) | Miscellaneous + Revision | 37-42 | Solve Misc Examples 23-26, attempt Miscellaneous Exercise, redo any wrong sums |
Total study time: 7.5 hours across four sittings. Students who attempt all four exercises in one sitting typically make 40% more sign errors in matrix multiplication on a topic test the next day.
How to Read This Chapter: A Recommended Reading Sequence
The the PDF are written in formal mathematical notation, line by line, in the same convention as the official NCERT print.
The chapter rewards a four-pass approach because matrix multiplication is a new operation for most students and its non-commutativity is the source of most exam errors.
- Pass 1 (Skim, 30 min): Read all five sections without pen and paper. The goal is to see the matrix definition, the operations ( + , scalar k · , product · ), and the transpose / symmetry definitions in one continuous flow.
- Pass 2 (Detailed, 90 min): Re-read with a pen. Write out the rule (AB)ij = k aik bkj by hand at least three times. Underline the compatibility condition (columns of A must equal rows of B) in every product example.
- Pass 3 (solved examples, 90 min): Solve every solved example WITHOUT looking at the solution first. Cover the page below the question. Compare your version with the book's version row by row, especially for 2× 2 and 3× 3 products.
- Pass 4 (Exercises, 150 min): Attempt Exercise 3.1, 3.2, 3.3, 3.4, and the Miscellaneous Exercise in that order. Skip nothing.
Related Links:
Author, Edition and Publisher Info for the Class 12th Maths Chapter 3 PDF
NCERT does not credit individual chapter authors. The chapter is part of the NCERT Class 12 Mathematics Part 1 textbook, jointly developed by the NCERT Mathematics Faculty Group.
| Field | Value |
|---|---|
| Title | Mathematics Part I, Textbook for Class XII |
| Publisher | National Council of Educational Research and Training (NCERT) |
| First Edition | 2006 |
| Current Edition | 2026-27 (Rationalised) |
| Pages (Chapter 3) | 42 |
| Language | English (also published in Hindi and Urdu) |
| ISBN (Part I) | 81-7450-629-2 |
More Matrices Mathematics Class 12 Resources
NCERT Book PDF for Class 12 Mathematics: All Chapters
Download any other chapter of the 2026-27 NCERT Class 12 Mathematics book using the table below.
| Chapter | Resource |
|---|---|
| Chapter 1 | Relations and Functions NCERT Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Book PDF |
| Chapter 4 | Determinants NCERT Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Book PDF |
| Chapter 6 | Application of Derivatives NCERT Book PDF |
| Chapter 7 | Integrals NCERT Book PDF |
| Chapter 8 | Application of Integrals NCERT Book PDF |
| Chapter 9 | Differential Equations NCERT Book PDF |
| Chapter 10 | Vector Algebra NCERT Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Book PDF |
| Chapter 12 | Linear Programming NCERT Book PDF |
| Chapter 13 | Probability NCERT Book PDF |
these 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 the chapter notes 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 the PDF is also available in Hindi - same page numbering, same equation labels.
- Formula PDF separate: The the resource formulas pdf is a one-page A4 reference sheet listing every identity used in the chapter.
- Solutions PDF separate: The chapter notes 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 the PDF 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 |
| matrices class 12 ncert solutions 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 matrices class 12 ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
- The these notes 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 this Class 12 page formulas reference sheet is the same A4 file students sometimes refer to as the resource all formulas - it lists every identity used in the chapter.
- State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board matrices class 12 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 this chapter solutions | State-board (Maharashtra HSC) phrasings; same core definitions. |
| Maharashtra board matrices class 12 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 the matrices class 12 ncert solutions 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.
This Collegedunia NCERT Class 12 Mathematics page is reviewed against every CBSE board paper release.
The Collegedunia Class 12 Maths team checks every formula on this page against the printed NCERT 2026-27 edition.
Matrices Class 12 PDF - Frequently Asked Questions
Ques. Where can I download the chapter notes for free?
Ans. You can download these notes Maths NCERT Book PDF directly from the the PDF. Both Normal and HD versions are available and both are free.
Ques. Is this this chapter aligned with the 2026-27 NCERT syllabus?
Ans. Yes. This page hosts these notes, and reflects the current 2026-27 syllabus for Class 12 Mathematics. The chapter now runs 42 pages with five numbered sections, after elementary row operations and the inverse-by-elementary-operations sub-topics were dropped from the new edition.
Ques. How many pages is the Class 12th Maths Matrices NCERT Book PDF?
Ans. The chapter PDF is 42 pages long and covers five sections (Introduction, Matrix, Operations on Matrices, Transpose, Symmetric and Skew-symmetric Matrices) plus a Miscellaneous Exercise.
Ques. How many solved examples and exercises does Class 12 Maths Chapter 3 have?
Ans. Chapter 3 contains 26 solved examples, Exercise 3.1, Exercise 3.2, Exercise 3.3, Exercise 3.4, and a Miscellaneous Exercise. All five are within the 2026-27 syllabus and all are CBSE-exam relevant.
Ques. What was removed from Chapter 3 Matrices in the new NCERT?
Ans. The current edition removed the sections on elementary row and column operations, inverse of a matrix using elementary operations, and the invertible-matrix uniqueness theorem. The inverse is now computed via adjoint in Chapter 4 Determinants.
Ques. How many marks does Matrices carry in CBSE Class 12 Maths Boards?
Ans. The chapter typically contributes 6 to 8 marks in the Class 12 Maths Board paper, usually split as one or two MCQs plus one short or long-answer proof on transpose properties or symmetric and skew-symmetric decomposition.
Ques. Is Matrices important for JEE Main?
Ans. Yes. Matrices contributes 6 to 8% of the JEE Main Mathematics section, with 2 to 3 questions per shift, typically clubbed with Determinants. Common stems include trace, transpose properties, idempotent or involutory matrices, and adjoint or inverse via determinant.
Ques. What is the difference between symmetric and skew-symmetric matrices?
Ans. A matrix A is symmetric if A' = A and skew-symmetric if A' = -A . Every square matrix can be uniquely written as the sum of a symmetric matrix 12(A + A') and a skew-symmetric matrix 12(A - A') .
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