Question

Matrices A and B will be inverse of each other only if ______.

Options

• AB = BA

• AB = 0, BA = I

• AB = BA = 0

• AB = BA = I

Answer 1

Matrices A and B will be inverse of each other only if AB = BA = I.

Explanation:

We know that if A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is said to be the inverse of A. In this case, it is clear that A is the inverse of B.

Thus, matrices A and B will be inverses of each other only if AB = BA = I.