If A and B are square matrices of size 'n' such that A2 - B2 = (A - B)(A + B), then which of the following will always be true?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → AB = BA
$A^2 - B^2 = (A - B)(A + B)$
$(A - B)(A + B) = A^2 + AB - BA - B^2$
$A^2 - B^2 = A^2 + AB - BA - B^2$
$AB - BA = 0$
$AB = BA$
The condition that always holds is $AB = BA$.