I'm trying to prove this but can't find the way.
What I think about is this: "We want to prove that $ab=ba$, i.e. if $aa=e$ , $a=a'$ where $a'$ is the inverse and $bb=e$, $b=b'$ where $b'$ is the inverse so $ab=(ab)'=b'a'=ba...$ but this is by definition. I can't reach the point how does it changes based on prime numbers.
Any help would be really appreciated.
For prime $p$, $\mathbb Z_p^×$ is cyclic... ($\therefore$ abelian)
It is also written $\mathbb Z_p^*$, since it is the multiplicative group of nonzero elements of the field $\mathbb Z_p$
In fact, $\mathbb Z_n^×$(the multiplicative group of units in $\mathbb Z_n$) is cyclic for $n=1,2,4$, a power of an odd prime or twice a power of an odd prime... (as Gauss knew, i believe...)