Hey guys! I'm having some trouble trying to solve this question.. Any advice/help is appreciated! 1. The problem statement, all variables and given/known data Suppose that a and b belong to a group such that: |a| = 4, |b| = 2, and suppose a3b=ba Find the order of ab. 2. Relevant equations 3. The attempt at a solution So I am unsure of which theorems I should be looking at... but anyways...... my horrible attempt: so a,b are in G. |ab| = (ab)n = 1 Let n = order(ab), anbn = 1 --> an=b-n I don't know if I should continue from this point because I don't know how exactly I would go about finding the order. I think |ab| = |ba|, yes or no? If it does then I'm guessing I can use that to find the order of a3b? Any hints or suggestions on how? Thank you.