Q10 of 74 Page 7

For the following pairs of matrices verify that (AB)–1 = B – 1A – 1:

A=

A = , |A| = 1


Then, adj A =


A – 1 =


B = , |B| = – 10


Then, adj B =


B – 1 =


Also, A.B =


AB =


|AB| = 936 – 946 = – 10


Adj(AB) =


(AB) – 1 =


Now B – 1A – 1 =


=


=


Hence, (AB) – 1 = B – 1 A – 1


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