Prove that real number pairs , where , with operation form a group.
With what kind of mathematical concept and operation this group coincide?
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.
so it has an identity.
so it has inverses.
I trust you can check associativity.