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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`

Text Solution

Verified by Experts

We have given
`A^2-A +I = 0`
Then we have to find the inverse of A
Let
`A^2-A +I = 0⟹A−A^2=I `
or `A(I−A)=I`
Therefore `A^(-1) =I-A`
Hence correct option is (d)
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