Proof: Let C be a Square Matrix, Show if C^(k+1)=0, then I-C is Nonsingular

[Luxe]

Homework Statement

Give a proof:
Let C be a square matrix.
Show if C^(k+1)=0,
then I-C is nonsingular and (I-C)^-1=I+C+C^2+...+C^k.

Homework Equations

I don't know.
I can't find a theorem that will help me.

The Attempt at a Solution

I know if a matrix is nonsingular, it has an inverse.

 

[csopi]

You need no theorem, one can see it directly, because , (I-C)(I+C+...+C^k)=I-C^(k+1)=I which means, that I-C is invertable, and the inverse is the above.