These NCERT notes for Matrices Class 12 Maths summarise every definition, operation and formula in Chapter 3. You can revise the whole chapter in one to two hours. The free notes PDF is available on this page.
The notes below follow the NCERT rationalised syllabus and CBSE guidelines for 2026-27.
- CBSE Class 12 Boards: 6 to 8 marks (10 to 13 marks in the Algebra unit with Determinants).
- JEE Main: Matrices and Determinants together give 2 to 3 questions, about 6 to 8% of the Maths section.
- CUET (UG) Maths: 2 to 3 direct MCQs on multiplication, transpose and inverse by row operations.
Every line of these Matrices Class 12 Notes is prepared by Collegedunia subject experts, mapped to the 2026-27 NCERT syllabus, and cross-checked against the last five CBSE papers plus JEE Main and CUET keys.
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Table of Contents |
Why these Matrices Class 12 Notes work for board exams
Matrices is an operations chapter. Once addition, multiplication, transpose and inverse click, the questions become procedural. These notes give you clean definitions and exam-ready formats.
- NCERT-faithful definitions for every matrix type, in marking-scheme wording.
- Solved formats for multiplication, transpose proofs and the symmetric-skew split.
- JEE and CUET callouts on inverse by elementary row operations and singular-matrix traps.
Matrices Class 12 Video Walkthrough
Source: Magnet Brains on YouTube
Matrices Class 12 Topic-by-Topic Breakdown
Here is the walkthrough in NCERT order, with the rules you must memorise.
- Order and equality: a matrix with m rows and n columns has order m × n. Two matrices are equal only when order and every entry match.
- Types: row, column, square, diagonal, scalar, identity and zero matrices. The only matrix that is both symmetric and skew-symmetric is the zero matrix.
- Multiplication: AB exists only when the columns of A equal the rows of B, and in general AB ≠ BA.
- Transpose: (AB)T = BT AT, the reversal law.
- Symmetric and skew-symmetric: any square matrix splits as A = 12(A + AT) + 12(A - AT).
- Inverse by EROs: reduce [A | I] to [I | A-1] using row operations only.
Matrices Class 12 Most Important Topics for Board, JEE and CUET
| NCERT Class 12 Maths Chapter 3: Important Topics | |
|---|---|
| Definition, order and equality | Row, column, square, diagonal, scalar matrices |
| Identity and zero matrices | Addition and scalar multiplication |
| Multiplication and non-commutativity | Transpose and its properties |
| Symmetric and skew-symmetric matrices | Symmetric-skew decomposition |
| Elementary row and column operations | Inverse by EROs (JEE) |
| Invertible matrices | Singular vs non-singular matrices |
Matrices Class 12 Weightage Across Chapters
| Chapter | Topic | Avg CBSE Marks |
|---|---|---|
| Ch 3 | Matrices | 6 to 8 marks |
| Ch 4 | Determinants | 6 marks |
| Ch 5 | Continuity and Differentiability | 8 marks |
| Ch 7 | Integrals | 10 marks |
| Ch 13 | Probability | 7 marks |
Matrices Class 12 Most Repeated Questions in Board Exams
- If A is a square matrix with A2 = A, find (I + A)3 - 7A. (CBSE 2020, 2023, 2024)
- Express a given 3 × 3 matrix as the sum of a symmetric and a skew-symmetric matrix. (CBSE 2019, 2022, 2024)
- Find the inverse of a 2 × 2 matrix using elementary row operations. (CBSE 2018, 2021, 2024)
- Show that BT A B is symmetric or skew-symmetric according to the nature of A. (CBSE 2020, 2023)
Matrices Class 12: Confusion Pairs Students Mix Up
| Often confused | The clean distinction |
|---|---|
| Order of product | (AB)T = BT AT, not AT BT. The reversal is mandatory. |
| Symmetric vs skew-symmetric | Symmetric: AT = A. Skew-symmetric: AT = -A, with all diagonal entries zero. |
| Singular vs non-singular | A matrix is invertible only when non-singular; a singular matrix has no inverse. |
| Zero product | AB = O does not force A = O or B = O. |
Matrices Class 12 Mistakes to Avoid in the Board Exam
- Skipping the compatibility check before writing a product; always state the orders first.
- Assuming AB = BA; so (A + B)2 = A2 + AB + BA + B2, not the binomial form.
- Forgetting the factor 12 in the symmetric-skew decomposition, which doubles both parts.
- Mixing row and column operations in the same inverse problem; pick one and stay with it.
Other Resources for Matrices Class 12
| Chapter | Notes | NCERT Solutions |
|---|---|---|
| Ch 1 Relations and Functions | Relations and Functions Notes | Relations and Functions Solutions |
| Ch 2 Inverse Trigonometric Functions | Inverse Trigonometry Notes | Inverse Trigonometry Solutions |
| Ch 3 Matrices | Matrices Notes | Matrices Solutions |
| Ch 4 Determinants | Determinants Notes | Determinants Solutions |
| Ch 5 Continuity and Differentiability | Continuity Notes | Continuity Solutions |
Exercise-wise Breakdown of the Matrices Chapter
| Exercise | Topic Tested |
|---|---|
| Exercise 3.1 | Order, types, equality of matrices |
| Exercise 3.2 | Addition, scalar multiplication, multiplication |
| 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 for the Matrices Notes
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading and quick revision | 2-3 MB |
| HD PDF | Print-ready desk study | 8-10 MB |
| Handwritten Notes PDF | Reading in a topper's handwriting | 5-7 MB |
Every definition and formula in the PDF matches the printed NCERT textbook. A Hindi-medium edition and a separate one-page formula sheet are also linked on the site.
How the Matrices Notes Pair with Solutions and the Formula Sheet
| Resource | Use it for | When |
|---|---|---|
| Notes (this page) | Theory, definitions, exam patterns | First pass, before practice |
| NCERT Solutions PDF | Step-by-step solved exercises | Second pass, during practice |
| Formula Sheet PDF | One-page identity recall | Third pass, with mock papers |
How to Use the Matrices Notes Page Effectively
- Sitting 1 (theory): read the NCERT chapter, mark every definition, then read the topic table above.
- Sitting 2 (examples): re-solve every solved example without looking, then check against the solutions PDF.
- Sitting 3 (exercises): attempt one exercise set per sitting and use the linked exercise pages to verify.
- Split revision roughly 60% NCERT and 40% JEE-style problems; for CUET focus on transpose and inverse MCQs.
Student Feedback - Class 12 Matrices Difficulty (Collegedunia Survey, March 2026):
- 73% of the students surveyed rated Matrices as one of the higher-weightage units in their CBSE preparation.
- Across 12,840 students, 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.
Matrices Class 12 Notes - Frequently Asked Questions
What is the weightage of Matrices in the CBSE Class 12 Maths Board Exam 2026?
Matrices alone carries 6 to 8 marks, and 10 to 13 marks when counted with Determinants in the Algebra unit.
Why is matrix multiplication not commutative?
The product depends on the order of rows and columns, so AB and BA usually differ and may even have different orders.
How do I express a matrix as symmetric plus skew-symmetric?
Write A as one half of (A + A transpose) plus one half of (A minus A transpose). The first part is symmetric and the second is skew-symmetric.
How do I find an inverse using elementary row operations?
Write A next to the identity as [A | I], then apply row operations until the left side becomes I. The right side is then the inverse.
Is the Matrices notes PDF free to download?
Yes. The notes PDF on this page is free, follows the 2026-27 NCERT syllabus, and is available in normal, HD and handwritten formats.
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