# Matrices Notes, Class 12 Mathematics | SwaVid

Matrices, NCERT Class 12 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers.

Canonical: https://www.swavid.com/cbse/class-12/maths/chapter/matrices

Source: https://www.swavid.com/cbse/class-12/maths/chapter/matrices

# Matrices

## Formulas and definitions

## Key ideas

## Common mistakes

## Quick checks

## Keep going

## Questions parents ask

## Class 12 Mathematics on SwaVid

### Matrix and its order

### Types of matrices

### Matrix operations

### Matrix multiplication

### Transpose of a matrix

### Symmetric and skew-symmetric matrices

### Next chapter

### Related chapter

### All chapters

SwaVid › CBSE › Class 12 › Mathematics › Matrices

Notes written by SwaVid from the NCERT textbook.

Class 12 Mathematics, Chapter 3. Key ideas, formulas and common mistakes.

CBSE does not print marks for a single chapter.

Short answer. This chapter introduces matrices, their representation, types, and basic algebraic operations like addition, scalar multiplication, and matrix multiplication. It explains the transpose of a matrix, and symmetric and skew-symmetric matrices.

Source: NCERT Mathematics Part I (Reprint 2026-27) , Chapter 3, Matrices

A matrix is an ordered rectangular array of numbers or functions. A matrix with m rows and n columns has order m × n and contains mn elements.

Common types include column matrix, row matrix, zero matrix, and square matrix. A square matrix is a diagonal matrix if non-diagonal elements are zero, a scalar matrix if diagonal elements are equal, and an identity matrix if diagonal elements are all 1.

Two matrices can be added or subtracted only if they have the same order. Multiplication of a matrix A by a scalar k multiplies every element of A by k.

The product AB of two matrices A and B is defined only if the number of columns of A equals the number of rows of B. Matrix multiplication is associative and distributive over addition, but generally not commutative.

The transpose A' or Aᵀ is formed by interchanging the rows and columns of A. If A is of order m × n, then A' is of order n × m.

A square matrix A is symmetric if A' = A, and skew-symmetric if A' = -A. Any square matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

Try each question first. Then tap it to see the answer.

Equate corresponding entries: x + y = 6 and xy = 8.

Express y in terms of x: y = 6 - x, then substitute into xy = 8 to get x(6 - x) = 8.

Solve x² - 6x + 8 = 0: (x - 2)(x - 4) = 0.

If x = 2 then y = 4, and if x = 4 then y = 2.

x = 2, y = 4 or x = 4, y = 2

Check orders: both matrices are 2 × 2, so the product AB is a 2 × 2 matrix.

First row: c₁₁ = (1)(2) + (2)(1) = 4, c₁₂ = (1)(0) + (2)(3) = 6.

Second row: c₂₁ = (3)(2) + (4)(1) = 10, c₂₂ = (3)(0) + (4)(3) = 12.

Assemble the product: AB = [4, 6; 10, 12].

[4, 6; 10, 12]

Write the transpose: A' = [3, 1; 5, -1].

Compute A + A' = [3 + 3, 5 + 1; 1 + 5, -1 + (-1)] = [6, 6; 6, -2].

Calculate (1/2)(A + A') = (1/2)[6, 6; 6, -2] = [3, 3; 3, -1].

[3, 3; 3, -1]

Determinants .

Linear Programming .

The 13 chapters of Class 12 Mathematics .

CBSE does not give marks to one chapter. It prints marks for units or parts, and the chapter list page shows them all.

No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed.

Determinants.

SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works.

- Ch 3 NCERT book
- 80 marks, theory paper
- 3 quick checks
- Assuming matrix multiplication is commutative . In general, AB ≠ BA even when both products are defined. Always maintain the given order of matrices when multiplying.
- Writing diagonal elements of a skew-symmetric matrix as non-zero values . For a skew-symmetric matrix, aᵢᵢ = -aᵢᵢ means 2aᵢᵢ = 0, so every diagonal element must be zero.
- Applying transpose directly without reversing the product order . Use the reversal rule (AB)' = B'A', not A'B'.
- Multiplying only the first row or column when multiplying by a scalar . A scalar k multiplies every single element in the matrix, so k[aᵢⱼ] = [k aᵢⱼ].

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