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

[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.

Thanks in advance! :)

 

[adriank]

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

 

[andreitta]

Thanks a lot for the quick reply! I solved it already :) Hadn't thought about the cardinal of
$$GL_n(\mathbb{F}_q)$$

Thanks!