Question

If A and B are square matrices of order m such that A² − B² = (A − B) (A + B), then which of the following is always correct?

Options

• A = B

• AB = BA

• A = 0 or B = 0

• A = I or B = I

Answer 1

AB = BA

Explanation:

A² − B² = (A + B)(A − B) 

A² − B² = A² − AB + BA − B²

A² − B² − A² + B² = − AB + BA

0 = − AB + BA

0 + AB = BA

Hence, AB = BA