Let A be a square matrix satisfying A^2+...

Let A be a square matrix satisfying `A^2+5A+5I= 0` the inverse of `A+2l` is equal to

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`A^2+5A+5I=0`
`A^2+5A+5I+I=I`
`A^2+5A+6I=I`
`A*A+2A+3A+6I=I`
`A(A+2I)+3I(A+2I)=I`
`(A+3I)(A+2I)=I`
`(A+2I)^(-1)=(A+3I)`.

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