# Math Help - Prove a group

1. ## Prove a group

Prove that real number pairs $(a, b)$, where $a\neq 0$, with operation $\circ$ form a group.
$(a, b) \circ (c,d)=(ac, ad + b)$.

With what kind of mathematical concept and operation this group coincide?

2. ## Group

You must show it is closed under the operation, has an identity, is closed under inverses, and is associative.

Closure is clear as + and * are closed in the reals, and R is a field, so it has no zero divisors. That is if a and c are not zero, their product is not zero.

$(a,b)\circ (1,0)= (a,b)$ so it has an identity.

$(a,b) \circ (1/a, -b/a)= (a/a, \frac{-ba}{a} + b)= (1,0)$
so it has inverses.

I trust you can check associativity.