Q10 of 74 Page 7

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


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