Solve for A-1 in Matrix Equation w/A, I

[rock.freak667]

Homework Statement

A square matrix A satisfies the matrix equation A³-3A²+7A-2I=0.
If A^-1 exists, find an expression for A^-1 in terms of A and I

Homework Equations

The Attempt at a Solution

I just multiplied the matrix equation by A^-1 and then rearranged to get

2A^-1 =3A-7I-A²

Is it that easy? Or is there something that I am missing?

 

[CompuChip]

Yes I suppose that is all, although you might want to check your signs.

 

[rock.freak667]

ok thanks..will do.