- #1
ossito_the-diracian
- 4
- 0
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.
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 can't get started
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 can't get started