Question

If $AandB$are square matrices of size $n\times n$ such that $A^2–B^2=(A–B)(A+B)$, then which of the following will be always correct?

• A. $AB=BA$
• B. either $AorB$ is a zero matrix
• C. either $AorB$ is an identity matrix
• D. $A=B$

Answer 1

The correct option is A

$AB=BA$

Explanation for the correct option:

Given:

$\begin{array}{rcl}{A}^2–B^2& =& (A–B)(A+B)\\ & =& A^2+AB–BA–B^2\\ & \Rightarrow & AB=BA\end{array}$

Hence, the correct answer is option A