Number of invertible/non-singular matrices over a finite field

1. Nov 30, 2008

andreitta

I'm trying to find the number of different non-singular matrices (nxn) over a finite field (order q). Any help would be greatly appreciated.

2. Nov 30, 2008

Have a look at this thread, which discusses the case where q = 2 and generalizes easily.

3. Nov 30, 2008

andreitta

$$GL_n(\mathbb{F}_q)$$

Thanks!