Question

Choose the correct alternative.

If A and B are square matrices of order n × n such that A² – B² = (A – B)(A + B), then which of the following will be always true?

Options

• AB = BA

• either of A or B is a zero matrix

• either of A and B is an identity matrix

• A = B

Answer 1

A² – B² = (A – B)(A + B)
∴ A² – B² = A² + AB – BA – B²
∴ 0 = AB – BA
∴ AB = BA.