Q. 204.0( 4 Votes )

# If , find the value of λ so that A^{2} = λA – 2I. Hence, find A ^{– 1}.

Answer :

A =

A^{2} =

=

Now, A^{2} = λA – 2I

= λA = A^{2} + 2I

=

= λ

=

= = 3 or λ = 1

So, A^{2} = 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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