Identity Matrices

A square matrix, I is an identity matrix if the product of I and any square matrix A is A.

IA = AI = A

For a 2 × 2 matrix, the identity matrix for multiplication is

When we multiply a matrix with the identity matrix, the original matrix is unchanged.

If the product of two square matrices, P and Q, is the identity matrix then Q is an inverse matrix of P and P is the inverse matrix of Q. (i.e. PQ = QP = I)

The inverse matrix of A is denoted by A ^-1. (read as “A inverse”)

AA^-1 = A^-1A = I

Note that the inverse of A^-1 is A.

Example:

Given that B is the inverse of A, find the values of x and y.

Solution:

AB =

Since B is an inverse of A, we know that AB = I

1 – 2y = 1
2y = 0
y = 0

2x = 1
x =

The following video explains more about identity matrix and inverse matrix.

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