Question

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

Options

• A² – B²

• A² – BA – AB – B²

• A² – B² + BA – AB

• A² – BA + B² + AB

Answer 1

If A and B are square matrices of the same order, then (A + B) (A – B) is equal to A² – B² + BA – AB.

Explanation:

(A + B)(A – B) = A(A – B) + B(A – B)

= A² – AB + BA – B²