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If A^(5)= 0 such that A^(n)ne I for 1 l...

If `A^(5)= 0` such that `A^(n)ne I ` for `1 le n le 4,` then `(I- A)^(-1)` is
equal to

A

`A^4`

B

`A^3`

C

`I+A`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`A^4(I-A)=A^4-A^5=A^4-O=A^4 ne I`
`A^3(l-A)=A^3-A^4 ne I`
`and , (I+A)(I-A)=I-A^2 ne I`
Hence, `(I-A)^(-1)ne A^4,A^3,I+A`.
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