This abstract problem appears not to have enough information.

[jdinatale]

I've put the problem and my attempt all in one image.

I would show the above using induction. But to show the order of the element in question, we need to know what power to raise the element to such that it equals the identity. I feel like the problem is missing information about the element b.

 

[Petek]

Your calculation of $(bab^{-1})^3$ has an error. Try to fix it. That should point you in the right direction.