If A^(3)=O, then prove that (I-A)^(-1) =...

If `A^(3)=O`, then prove that `(I-A)^(-1) =I+A+A^(2)`.

A

`I-A`

B

`(I-A)^(-1)`

C

`(I+A)^(-1)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

B

We have,
`(I-A)(I+A+A^2)=I+A+A^2-A-A^2-A^3=I-O=I`
`:. (I-A)^(-1)=I+A+A^2`

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