For the following pairs of matrices verify that (AB)–1 = B – 1A – 1:
|A| = 1
Adj A =
A – 1 =
B =
|B| = – 1
B – 1 =
Also, AB =
=
|AB| = 407 – 406 = 1
And, adj(AB) =
(AB) – 1 =
Now, B – 1A – 1 =
Hence, (AB) – 1 = B – 1A – 1