If A and B are square matrices of the same order, then (A + B)(A – B) is equal to

Question

Philoid · Accepted Answer

(A + B)(A – B) = A (A – B) + B (A – B)

= A.A – A.B + B.A – B.B

=A² – A.B + B.A – B.B

= A² – AB + BA – BB

Matrix multiplication does not have a commutative property i.e.., A.B ≠ B.A

Hence, Option (C) is the answer.