Q. 255.0( 2 Votes )

Show that the matrix, satisfies the equation, A3 – A2 – 3A – I3 = O. Hence, find A–1.

Answer :

A =


A3 = A2.A


A2 =


=


A2.A =


=


=


Now, A3 – A2 – 3A – I



=


=


=


Thus, A3 – A2 – 3A – I


Now, (AAA) A – 1. – (A.A) A – 1 – 3.A A – 1 – I.A – 1 = 0


AA(A – 1A) – A(A – 1A) – 3(A – 1A) = – 1(A – 1I)


A2 – A – 3A – I = 0


= A – 1 =


Now,



=


=


=


Hence, A – 1 =


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