question_answer 1)

Let , verify that (AB)?1       = B?1 A?1.  

Answer:

            is non-singular matrix so A?1 exists       A11 = (?1)1+1 . 5 = 5; A12 (?1)1+2.2 = ?2                   A21 = (?1)2+1 . 7 = ?7; A22 (?1)2+2.3 = 3                         Also        is also non-singular so B?1 exists.        B11 = (?1)1+1 . 9 = 9       B12 = (?1)1+2. 7 = 7       B21 = (?1)2+1. 8 = ?8       B22 = (?1)2+2. 6 = 6                                       ?.. (1)       Now       And adj (AB) = adj B. adj                   From (1) and (2), we get (AB)?1 = B?1 A?1