NCERT Exemplar Class 12 Maths Chapter 3: Matrices. NCERT Exemplar Solutions for Class 12 Maths Chapter 3 Matrices prepare students for their Class 12 exams thoroughly.

Maths problems and solutions for the Class 12 pdf are provided here which are similar to the questions being asked in the previous year’s board.

## NCERT Exemplar Class 12 Maths Chapter 3: Matrices

3.1 Overview
3.1.1 A matrix is an ordered rectangular array of numbers (or functions). For example,

The numbers (or functions) are called the elements or the entries of the matrix. The horizontal lines of elements are said to constitute rows of the matrix and the vertical lines of elements are said to constitute columns of the matrix.

3.1.2 Order of a Matrix

A matrix having m rows and n columns is called a matrix of order m × n or simply m × n matrix (read as an m by n matrix).In the above example, we have A as a matrix of order 3 × 3 i.e., 3 × 3 matrix.
In general, an m × n matrix has the following rectangular array :

The element, aij is an element lying in the ith row and jth column and is known as the (i, j)th element of A. The number of elements in an m × n matrix will be equal to mn.

3.1.3 Types of Matrices

(i) A matrix is said to be a row matrix if it has only one row.
(ii) A matrix is said to be a column matrix if it has only one column.

Two matrices can be added if they are of the same order.

3.1.5 Multiplication of Matrix by a Scalar

3.1.6 Negative of a Matrix

The negative of a matrix A is denoted by –A. We define –A = (–1)A.

3.1.7 Multiplication of Matrices

The multiplication of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B.

Notes:
1. If AB is defined, then BA need not be defined.
2. If A, B are, respectively m × n, k × l matrices, then both AB and BA are defined if and only if n = k and l = m.
3. If AB and BA are both defined, it is not necessary that AB = BA.
4. If the product of two matrices is a zero matrix, it is not necessary that one of the matrices is a zero matrix.
5. For three matrices A, B and C of the same order, if A = B, then AC = BC, but converse is not true.
6. A. A = A2 , A. A. A = A3, so on.

3.1.8 Transpose of a Matrix

3.1.9 Symmetric Matrix and Skew Symmetric Matrix

Note : Diagonal elements of a skew symmetric matrix are zero.

3.1.10 Invertible Matrices

3.1.11 Inverse of a Matrix using Elementary Row or Column Operations