Proving I-A is Invertible with A^m=0

[Fosheimdet]

Homework Statement

Let A be a nxn matrix, and I the corresponding identity matrix, both in the real numbers ℝ. Assume that A^m=0 for a positive integer m. Show that I-A is an invertible matrix.

Homework Equations

The Attempt at a Solution

 

[lurflurf]

Hint what is

$$\sum_{j=0}^m \, A^j$$

what is

$$(I-A)\sum_{j=0}^m \, A^j$$