Reduced Residue System under Multiplication forms Abelian Group/Proof 3

Proof
Taking the group axioms in turn:

G0: Closure
From Modulo Multiplication on Reduced Residue System is Closed:


 * $\left({\Z'_m, \times}\right)$ is closed.

G1: Associativity
We have that Modulo Multiplication is Associative.