If A and B are square matrices of order 3, then

adj(AB) = adj A + adj B (A + B)–1 = A–1 + B–1 AB = O ⇒ |A| = 0 or |B| = 0 AB = O ⇒ |A| = 0 and |B| = 0

AB = O ⇒ |A| = 0 or |B| = 0

If AB = O then either of A and B are necessarily singular Hence (3) is the correct answer.