Q26 of 74 Page 7

If . Verify that A3 – 6A2 + 9A – 4I = O and hence fid A – 1.

A =


A3 = A2.A


A2 =


=


A2.A =


=


=


Now, A3 – 6A2 + 9A – 4I



=


=


Thus, A3 – 6A2 + 9A – 4I


Now, (AAA) A – 1. – 6(A.A) A – 1 + 9.A A – 1 – 4I.A – 1 = 0


A2 – 6A + 9I = 4A – 1


= A – 1 =


Now,



=


=


=


Hence, A – 1 =


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