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I have tried for $GL(2,\mathbb{Z}_p)$ its $= (p^2-1)(p^2-p)$ Since as number of ways in which first row can be filled is $p^2-1$ by omitting the way in which all entries r zero and second row can be filled in $p^2-p$ ways by omitting the ways in which d entries are multiples of first row. I have also tried for for $GL(3,\mathbb{Z}_p)$ its found as $=(p^3-1)(p^3-p)(p^3-2p)$. Is it right?

E.Lim
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Sajan Phutela
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    The last factor is $p^3-p^2$, since the span of the first two columns (they span a two-dimensional space) is not allowed. – MooS Jan 07 '16 at 16:55
  • The size of the group $GL(n,q)$ is $(q^n-1)(q^n-q)\cdots (q^n-q^{n-1})$, where $n$ and $q$ are positive integers. – A-213 Jan 07 '16 at 20:53

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