Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
8 pages · 7 hand-drawn matrix diagrams · 10 boxed key results · Class 12 Maths Chapter 3, 2026-27 NCERT
- CBSE Weightage: 5 to 7 marks (Matrices + Determinants together carry 10 to 12 marks; one short answer plus one MCQ / case-study on order, operations, or symmetric decomposition)
- JEE Main Weightage: 6 to 8% (2 to 3 questions per shift on matrix multiplication, inverse, symmetric / skew-symmetric, and elementary transformations)
- JEE Main Weightage: Not in JEE Main syllabus (Maths-only chapter; high weight for JEE Main, JEE Advanced, and CUET)
Matrices Handwritten Notes: Complete Diagram List for Class 12 Maths
| Page | Diagram | What It Shows |
|---|---|---|
| 1 | Generic m × n matrix grid with index labels | The A = [aij]m × n grid with rows and columns highlighted; explains the i-row j-column index convention |
| 2 | Six matrix-type grid panel | Row, column, square, diagonal, scalar, identity, and zero matrix shown as 6 small grids side-by-side with their compact symbols |
| 3 | Order-compatibility chart for multiplication | Two-grid sketch showing A(m × n) · B(n × p) = C(m × p) with the inner indices matching and outer indices forming the product order |
| 4 | Solved row-times-column multiplication arrow | A 2 × 3 times 3 × 2 example with arrows highlighting how row-1 of A is dotted with column-1 of B to give the (1,1) entry of AB |
| 5 | Symmetric vs skew-symmetric grid pair | Side-by-side 3 × 3 grids: symmetric has matching off-diagonal values, skew-symmetric has negatives plus zero diagonal |
| 6 | Symmetric + skew decomposition flow | Hand-drawn arrows showing A = ½(A + A′) + ½(A − A′), labelling each half as symmetric and skew respectively |
| 8 | Summary learn table | Ten-row condition table for order, types, operations, transpose, symmetric, skew-symmetric, invertibility, and elementary operations |
Quick Tip: Copy the order-compatibility chart (page 3) and the symmetric + skew decomposition flow (page 6) on the back of your answer sheet during revision; CBSE has asked at least one matrix multiplication or symmetric-decomposition question in every Board paper since 2022.
Matrices Video Walkthrough
Source: Magnet Brains on YouTube
Matrices Class 12 Chapter 3 NCERT Exercise-Wise Snapshot
| Sub-Topic | NCERT Qs | Typical CBSE Marks |
|---|---|---|
| Order, Notation, and Six Standard Types | 10 | 1 to 2 |
| Equality of Matrices and Element Comparison | 4 | 1 to 2 |
| Addition, Subtraction, Scalar Multiplication | 12 | 2 to 3 |
| Matrix Multiplication and Properties | 14 | 3 to 5 |
| Transpose and Its Properties | 6 | 2 to 3 |
| Symmetric and Skew-Symmetric Decomposition | 8 | 3 to 5 |
| Elementary Operations and Inverse | 8 | 3 to 5 |
Matrices Top 8 Key Results for Class 12 Maths Quick Recall
| Concept | Result / Test |
|---|---|
| Matrix Order | A = [aij]m × n has m rows and n columns; total elements = mn |
| Equality of Matrices | A = B iff same order AND aij = bij for every i, j |
| Multiplication Order Rule | Am × n · Bn × p = (AB)m × p ; inner indices must match |
| Non-Commutativity | AB ≠ BA in general; AB = AC does NOT imply B = C (no cancellation law) |
| Transpose Properties | (A')' = A, (A + B)' = A' + B', (kA)' = kA', (AB)' = B'A' |
| Symmetric Matrix | A' = A , i.e. aij = aji for every i, j |
| Skew-Symmetric Matrix | A' = -A , i.e. aij = -aji ; diagonal entries are all 0 |
| Inverse Criterion | A square matrix A is invertible iff there exists B such that AB = BA = I ; B is unique and written A-1 |
Matrices Class 12 Maths Self-Assessment Quick Quiz
Q1. If A is a matrix of order 3 × 4 and B is a matrix of order 4 × 5 , then the order of AB is:
Q2. If A is a skew-symmetric matrix of order 3 , then the sum of its diagonal entries is:
Q3. If A and B are symmetric matrices of the same order, then AB - BA is:
Q4. The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is:
Q5. If A = bmatrix 1 & 2 3 & 4 bmatrix , then A + A' is:
Class 12 Maths Chapter 3 Matrices PYQ Snapshot (2026 to 2021)
| Topic | Asked in | Typical Marks |
|---|---|---|
| Express a given matrix as sum of a symmetric and a skew-symmetric matrix | CBSE 2025, 2024, 2023, 2022, JEE Main 2025, 2023 | 3 to 5 |
| Find AB given two matrices (often 2 × 3 and 3 × 2) and verify a property like (AB)′ = B′A′ | CBSE 2025, 2024, JEE Main 2025, 2024, 2022 | 3 to 5 |
| Find inverse of a 2 × 2 or 3 × 3 matrix using elementary row operations | CBSE 2024, 2023, 2022, JEE Main 2024, 2023 | 3 to 5 |
Matrices Weightage Compared Across Class 12 Maths Chapters
Ch 1 Relations and Functions
5 marks
Ch 2 Inverse Trigonometric Functions
4 marks
Ch 3 Matrices
6 marks
Ch 4 Determinants
6 marks
Ch 5 Continuity and Differentiability
8 marks
Ch 6 Application of Derivatives
6 marks
Ch 7 Integrals
9 marks
Ch 8 Application of Integrals
4 marks
Ch 9 Differential Equations
5 marks
Ch 10 Vector Algebra
5 marks
Ch 11 Three Dimensional Geometry
5 marks
Ch 12 Linear Programming
5 marks
Ch 13 Probability
6 marks
Other Resources
NCERT Handwritten Notes for Class 12 Maths: All Chapters
| Chapter | Resource |
|---|---|
| Chapter 3 | Matrices Handwritten Notes |
| Chapter 1 | Relations and Functions Handwritten Notes |
| Chapter 2 | Inverse Trigonometric Functions Handwritten Notes |
| Chapter 4 | Determinants Handwritten Notes |
| Chapter 5 | Continuity and Differentiability Handwritten Notes |
| Chapter 6 | Application of Derivatives Handwritten Notes |
| Chapter 7 | Integrals Handwritten Notes |
| Chapter 8 | Application of Integrals Handwritten Notes |
| Chapter 9 | Differential Equations Handwritten Notes |
| Chapter 10 | Vector Algebra Handwritten Notes |
| Chapter 11 | Three Dimensional Geometry Handwritten Notes |
| Chapter 12 | Linear Programming Handwritten Notes |
| Chapter 13 | Probability Handwritten Notes |
Student Feedback - 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.
Class 12 Maths Handwritten Notes PDF - Frequently Asked Questions
Ques. Where can I download the Class 12 Maths Handwritten Notes PDF for free?
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