You should phrase the question more precisely. It doesn't make sense to say that a matrix is isomorphic to a group. What would this mean anyway? What you (probably) mean is that the group generated by that matrix is isomorphic to some familiar group. Also, you should specify the operation on your matrix, which in this case is (probably) ordinary matrix multiplication.

Let A be that matrix (which I suppose is:

1 b

0 1

).

Then notice how is

1 2b

0 1,

and similarly is

1 nb

0 1.

It sure looks like we are getting the integers in this way. Try defining an isomorphism from the group generated by A to the group of integers with addition, and remember to consider the inverses (which I didn't).