Let SL(2,Z) be the set of 2x2 matrices with integer coefficients.(adsbygoogle = window.adsbygoogle || []).push({});

I know that SL(2,Z) is generated by S and T, where

S= (0 -1

1 0)

and T= (1 1

0 1).

But how can I show that everyone element of G (the group generated by S and T) is in SL(2,Z)?

Also, let FcH (upper half-plane) be defined as F= {z in C: abs(z)>1, abs(Re(z)<1/2)}.

How can I draw a picture of F? Which linear fractional transformations correspond to S and T (as given above)?

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# Sl(2,z) matrices with integer coefficients

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