# Matrix property proof

Tags:
1. Oct 27, 2015

### AllRelative

1. The problem statement, all variables and given/known data
Show that no matrix A ∈ M3 (ℝ) exists so that A2 = -I3

2. Relevant equations

3. The attempt at a solution
This is from a french text book of first year linear algebra. I'm quite familiar with properties of matrices but I don't have any idea of how to prove this.

Thanks for the help!

2. Oct 27, 2015

### andrewkirk

Think about the determinants in the given equation.

3. Oct 27, 2015

### fzero

Compute the determinant of $A$.

4. Oct 27, 2015

### AllRelative

I took me a while but I got it. Thanks both of you!