Q20 of 98 Page 314

For square matrices A and B of the same order, we have adj(AB)=?

We know that (AB)^-1 = adj(AB)/

adj (AB)= (AB)^-1

We also know that (AB)^-1 = B^-1. A^-1

Putting them in 1

Adj (AB) = B^-1. A^-1.

= (A^-1.) (B^-1)

= adj(A) adj(B)

Since, adj (A)= (A)^-1

adj (B)= (B)^-1

If A and B are symmetric matrices of the same order then (AB – BA) is always

Matrices A and B are inverse of each other only when

If A is a 3-rowed square matrix and │A│=4 then adj(adj A)=?

If A is a 3-rowed square matrix and │A│=5 then │adj A│=?