Binary operations on groups

Hey guys,

I am trying to prove that a set with the specified binary operation below is a group? Here is the problem

on R* x R, (a, b) * (c,d) = (ac, bc + d)

I know that I have to prove that it is has

1.) an identity: a * x = a

2.) an inverse: a * x = e

3.) associative

The thing that throws me off is the (ordered pair). How do I start it off?

This is how I started off trying to prove the identity

a*x = a

(a,b) * (x1, x2) = (a,b) ?? DOn't know if I can use x1,x2 ??

(a*x1, b*x1 + x2 ) = (a,b)

then I get two equations:

a *x1 = a --> x1 = 1

b*x1 + x2 = b --> b*1 + x2 = b --> x2 = 0

NOw I plug x1 and x2 back into original eqn:

(a *1, b*1 + 0 ) = (a, b)

(a,b) = (a,b)

haha, I started off not knowing how to go about and the mere fact of coming to this site and trying to ask a question got me going in the right direction and I ended up solving my own problem, (Clapping). My thanks for this website!