## Another abstract problem

Hi,

Question is:

GL(2,R) is the set of all 2x2 matrices with real entries and non-zero determinant. It is a group with matrix multiplication as operation.
Let GL(2,Q) and GL(2,Z) denote the subsets of GL(2,R) consisting of 2x2 matrices with non-zero determinant an entries in Q and Z respectively.
a) Is GL(2,Q) a subgroup of GL(2,R)? If yes, identity the identity and the inverse of a generic element.
b) Is GL(2,Z) a subgroup of GL(2,R)? If yes, identify the identity and the inverse of a generic element.

Any ideas?

Thanks