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Possible Duplicate:
Groups/Linear maps

Given a natural number $n$, consider the set of all $n\times n$ matrices where each element is a member of $\mathbb Z_p$, where $p $ is a prime.

How many of these matrices are invertible modulo $p$?

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    This is more or less the same question as http://math.stackexchange.com/questions/64454/counting-automorphisms/64455#64455.2012-03-09
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    This is the Gaussian Binomial Coefficient, $\displaystyle \binom n 0_p$2012-03-09
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    ${\rm GL}(n, \mathbb{Z})$: http://en.wikipedia.org/wiki/General_linear_group#Over_finite_fields2012-03-09
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    Answered at http://math.stackexchange.com/questions/34271/groups-linear-maps2012-03-09
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    The same idea from [this answer](http://math.stackexchange.com/q/116216/742) works as well.2012-03-09

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