I am trying to solve this problem for homework but unable to get anything. The question is to find the number of invertible 2x2 matrices in mod p? Each entery can bee from the set {0,1,2....(p-1)}
where p is prime.
how many 2x2 matrices are invertible in mod p
1
$\begingroup$
arithmetic
modular-arithmetic
permutations
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1Right, I was asking those as hints to you mainly. It's just a counting problem once you interpret invertibility the right way. The answer below is precisely was I was getting at. – 2012-11-19
1 Answers
5
The answer is $(p^2-1)(p^2-p)$, since there are $(p^2-1)$ ways to choose the first column such that it is non-zero, then the second column can be chosen in any way out of the $p$ multiples of the first column.
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0What about if there is an additional constraint that the matrices be unimodular? My estimate is $(p^2-1)*2p$. – 2017-02-24