If A^(2)-A+I=O, then A^(-1) is equal to...

If `A^(2)-A+I=O`, then `A^(-1)` is equal to

A

`A^(-2)`

B

`A + I`

C

`I - A`

D

`A - I`

Verified by Experts

The correct Answer is:

C

`A^(2) -A+I=0`
` rArr I=A-A^(2) rArr I = A(I-A)`
`rArr A^(-1) I = A^(-1) (A(I-A))rArr A^(-1) =I - A`

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