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If A^5=O such that A^n != I for 1 <= n <...

If `A^5=O` such that `A^n != I` for `1 <= n <= 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
`A^(4) (I-A) = A^(4) I - A^(5)=A^(4) - 0 = A^(4) ne I`
`A^(3) (I-A) = A^(3) I- A^(4) = A^(3) - A^(4) ne I`
`(I + A) (I-A) = I^(2) - A^(2) = I -A^(2) ne I`
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