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If A^2-A +I = 0, then the inverse of A i...

If `A^2-A +I = 0`, then the inverse of A is: (A) `A+I` (B) `A` (C) `A-I` (D) `I-A`

A

`A^(-2)`

B

`A+I`

C

`I-A`

D

`A-I`

Text Solution

Verified by Experts

The correct Answer is:
C
`A^(2)=A+I=0`
or `I=A-A^(2)`
`IA^(-1)=A A^(-1)-A^(2)A^(-1)`
`implies A^(-1)=I-A`
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