I'm not quite sure what this question is asking.

Problem:Let a and b be elements of a group G. Show that if ab has finite order n, then ba also has order n.

It is my understanding that the order ofgroupis simply the number of elements in the group, and the order of ageneratoris the number of elements in the set it generates. But... what is the order of any oldelementin G, like the question asks?