Q24 of 74 Page 7

For the matrix . Show that A3 – 6A2 + 5A + 11I3 = O.Hence, find A – 1.

A =


A3 = A2.A


A2 =


=


A2.A =


=


=


Now, A3 – 6A2 + 5A + 11I


+ 11


=


=


=


Thus, A3 – 6A2 + 5A + 11I


Now, (AAA) A – 1. – 6(A.A) A – 1 + 5.A A – 1 + 11I.A – 1 = 0


AA(A – 1A) – 6A(A – 1A) + 5(A – 1A) = – 1(A – 1I)


A2 – 6A + 5I = 11 A – 1


= A – 1 =


Now,


A2 – 6A + 5I


=


=


=


=


Hence, A – 1 =


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