Hey phys251.
Could you show this by exhaustion (since you only have four elements)?
Given |G| = 4, we are to show G is abelian (commutative).
The proof wants me to start by assuming the existence of x in G s.t. o(a) = 4, and in that case, G is abelian. (Further cases follow.)
How? All I can figure from that is that a = e.