Definition: A set of numbers (real or complex) presented in the form of a rectangular array having m rows and n columns is called m x n matrix.

We write a m x n matrix as

Where m = no of rows

and n = no of columns

Square matrix: A matrix in which the no. of rows (m) = no. of columns (n) is known as a square matrix.

Example: The matrix

 is a square matrix.

Unit matrix or Identity matrix: A square matrix in which the diagonal elements are 1 is called a unit matrix or Identity matrix. It is denoted by I.

Example: The matrix

 is a unit matrix or order 3.

Diagonal matrix: A square matrix having only the diagonal elements and remaining all the other elements are zero is known as diagonal matrix.

Example: The matrix

 is a diagonal matrix.

Column matrix: It is a matrix which has single column and m no. of rows.

Example:

 is a column matrix of order (4 x 1)

Row matrix: A matrix which has single row and n no. of columns is known as row matrix.

Example:

 is a row matrix of order (1 x 4)

Addition of matrix: The sum can be obtained by adding the corresponding elements of matrix [A] and [B]. For addition, the two matrices should be of the same order.

Example:

Let

and

then =

Subtraction of matrix: The subtraction can be obtained by subtracting the corresponding elements of matrix [A] and [B]. For subtraction, the two matrices should be of the same order.

Example:

Let

and

then =

Matrix multiplication:  For multiplication of two matrices, the columns (n) of matrix [A] should be equal to the rows of matrix [B].

Example:

Let  and

so =