/*
M11 as 10 x 10 matrices over Z.
*/

F:=RationalField();

G<x,y>:=MatrixGroup<10,F|\[
0,1,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,0,1,0]
,\[
1,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,
0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,1,0,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
0,0,0,0,0,0,0,0,0,1]
>;

a:=x;b:=y;