The group {[1 a
0 1 ] l a Є Z} is isomorphic to what familiar group? I'm not really sure how to go about this other than just choosing groups and testing if they are isomorphic. Is there any way to narrow it down?
The problem is that I don't know what groups you are "familiar" with!
But I would suggest that before you start "choosing groups and testing" you look at the properties of members of this group. In particular, is the operation matrix addition or multiplication? What is the identity? What is the inverse of a general member?