i have a question about elements in SL(2,Z3), a,b,c,d are intergers and ad-bc=1 or Det [A]=1. i have to write all the matrices of this group and prove that I do have all of them.(adsbygoogle = window.adsbygoogle || []).push({});

i know that only 3 elements exists in Z3 {[0],[1],[2]} with all others just being repeats. i.e. [-3]=0, [[4]=[1].

i can write 24 elements with ad-bc=1,

i.e. [[1,2],[2,2]] which is [1][2]-[2][2]=[2]-[4]=[-2]=[1]

my problem is that i can't quite write WHY i have found all elements and they are no more, i was trying to appraoch i using contradiction but cant get started

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# Abstract alg - SL(2,Z3)

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