Question

If A and B are two non-singular square matrices of the same order, the adjoint of AB is equal to

(A) (adj A) (adj B)

(B) (adj B) (adj A)

(C) adj(BA)

(D) adj A + adj B

Answer 1

Answer is (B) (adj B) (adj A)

A and B are non-singular, so AB is non-singular.

Hence AB adj(AB) = |AB| I (1)

AB(adj B adj A) = A(B adj B) adj A

= A(|B| I) adj A

= |B| (A(adj A))

= |B| |A| I (2)

adj(AB) = (adj B) (adj A)