Consider the set of matrices {[1] (a) Prove that if a GL(Z), then there exists y E GL2(Z) such that [1 GL(Z) = a, b, c, d e Z and ad-bc= te=1} xy=yx = 1, where I = (b) Prove that if ,2 GL2(Z), then 12 GL(Z). [Remark: this shows that GL2(Z) is a subgroup of GL(R).]