Q20 of 35 Page 4

If , find the value of λ so that A2 = λA – 2I. Hence, find A – 1.

A =


A2 =


=


Now, A2 = λA – 2I


= λA = A2 + 2I


=


= λ


=


= = 3 or λ = 1


So, A2 = A – 2I


Multiply by A – 1 both sides


= A.A. A – 1 = A. A – 1 – 2I. A – 1 = 0


= 2A – 1 =


Hence, A – 1 =

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