So the relation would be between sets of x and y. However the problem I see is that any two x and y are equivalent if we are talking . Possibly this would be some sort of "maximal" relation? (My ignorance here is probably going to make a fool out of me, so I'm likely done trying to help out on this one.)
A) Reflexive: xRx by choosing z=1.
B) Symmetric: xRy implies there exists z such that x = yz. But x=yz => y = x(1/z) . Thus yRx.
A) Transitive: xRy , yRw => there exists a and b such that x =ay and y = bw. But this means x = ay = a(bw) = (ab)w. Thus xRw.