Question

If A and B are square matrices of the same order, then which of the following statements is/are always true?

1. (A + B) (A – B) = A² – B²
2. AB = BA
3. (A + B)² = A² + AB + BA + B²
4. AB = 0 ⇒ A = 0 or B = 0

Options

• Only (i) and (iii)

• Only (ii) and (iii)

• Only (iii)

• Only (iii) and (iv)

Answer 1

Only (iii)

Explanation:

(A + B)² = (A + B) (A + B)

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

= A² + AB + BA + B²