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

  1. 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! :)
     
  2. jcsd
  3. Have a look at this thread, which discusses the case where q = 2 and generalizes easily.
     
  4. Thanks a lot for the quick reply! I solved it already :) Hadn't thought about the cardinal of
    [tex] GL_n(\mathbb{F}_q) [/tex]

    Thanks!
     
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