If A and B are square matrices of order 3, then | MATH - SPECIAL TYPES OF MATRICES, TRANSPOSE, ADJOINT AND INVERSE OF MATRICES | SolveeIt | Solveeit

Today, August 19

Question

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

A

adj(AB) = adjA + adjB

B

(A + B)^–1 = A^–1 + B^–1

C

AB = O ⇒ |A| = 0 or |B| = 0

D

AB = O ⇒ |A| = 0 and |B| = 0

Answer

AB = O ⇒ |A| = 0 or |B| = 0

Explanation

Solution

If AB = O then either of A and B are necessarily singular