# Linear Algebra proof

1. Sep 15, 2013

### Fosheimdet

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution

2. Sep 15, 2013

### lurflurf

Hint what is

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

what is

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