Question

Which of the following properties is/are true for two matrices of suitable orders?

1. (A + B)′ = A′ + B′
2. (A − B)′ = B′ − А′
3. (AB)′ = A′B′
4. (kAB)′ = kB′A′ (k is a scalar)

Options

• (i) only

• (i), (ii) and (iii)

• (i) and (ii)

• (i) and (iv)

Answer 1

(i) and (iv)

Explanation:

(A + B)′ = A′ + B′ is always true. Also, the transpose of scalar multiplication and product gives (kAB)′ = k(AB)′ = kB′ A′, matching option (iv). However, (A − B)′ = A′ − B′, not B′ − A′, and (AB)′ = B′ A′, not A′ B′.