Question

If $A$ and $B$ are square matrices of order $n\times n$ such that $A^2-B^2=(A-B)(A+B),$ then which of the following will be always true?

• A. $AB=BA$
• B. Either of $A$ or $B$ is a zero matrix.
• C. Either of $A$ or $B$ is identity matrix.
• D. $A=B$

Answer 1

The correct option is A $AB=BA$

Given:

$A^2-B^2=(A-B)(A+B)$
$\Rightarrow A^2-B^2=A^2-B^2+AB-BA$

Only possibility when, $AB=BA$

Hence, option A.