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

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

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Given`A^(3)=O`
Now, `(I-A) (I+A+A^(2))`
`=I^(2)+IA+IA^(2)-AI-A^(2)-A^(3)`
`=I+A+A^(2)-A-A^(2)-O`
`=I`
`:. (I-A)^(-1)=I+A+A^(2)`
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