A matrix represents a collection of numbers arranged in an order of rows and columns. It is necessary to enclose the elements of a matrix in parentheses or brackets.
A matrix with 9 elements is shown below.

This Matrix [M] has 3 rows and 3 columns. Each element of matrix [M] can be referred to by its row and column number. For example, a₂₃=6

Order of a Matrix:

The order of a matrix is defined in terms of its number of rows and columns.
Order of a matrix = No. of rows ×No. of columns
Therefore Matrix [M] is a matrix of order 3 × 3.

Transpose of a Matrix :

The transpose [M]^T of an m x n matrix [M] is the n x m matrix obtained by interchanging the rows and columns of [M].
if A= [a_ij] mxn , then A^T = [b_ij] nxm where b_ij = a_ji

Properties of transpose of a matrix:

• (A^T)^T= A
• (A+B)^T= A^T + B^T
• (AB)^T= B^TA^T

Singular and Non-singular Matrix:

1. Singular Matrix: A square matrix is said to be singular matrix if its determinant is zero i.e. |A|=0
2. Nonsingular Matrix: A square matrix is said to be non-singular matrix if its determinant is non-zero.