If A and B are square matrices of size n × n such that

• Matrices Determinants

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

1. either A or B is an identity matrix
2. either A or B is a zero matrix
3. AB = BA
4. A = B

Answer

Given,

A² – B² = (A + B)(A – B)

This implies, 0 = BA – AB

The correct option is C.