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
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