Let $G$ be a group and $a,b∈G$. Suppose order of $(ab)$ in $G$ is $n$. Show that $(ba)^n=e$ Prove that the order of $(ba)$ in $G$ is $n$.
Show that if $ab$ has finite order $n$, then $ba$ also has order $n$. - Fraleigh p. 47 6.46.