Show that if $n$ is a positive integer and $a$ and $b$ are integers relatively prime to $n$ such that $\left(\operatorname{ord}_{n} a, \operatorname{ord}_{n} b\right)=1$, then $\operatorname{ord}_{n}(a b)=\operatorname{ord}_{n} a \cdot \operatorname{ord}_{n} b$.