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

1. ### andreitta

7
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! :)

534
Have a look at this thread, which discusses the case where q = 2 and generalizes easily.

3. ### andreitta

7
Thanks a lot for the quick reply! I solved it already :) Hadn't thought about the cardinal of
$$GL_n(\mathbb{F}_q)$$

Thanks!

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