1. The problem statement, all variables and given/known data Show that for any rings R and S, R x S and S x R are isomorphic, and A x B is the cartesian product, or ordered pairs. So an element of R x S can be written as (r1, s1). 2. Relevant equations 3. The attempt at a solution So I have to show that there is a bijection from R x S to S x R, and this bijection must preserve addition and multiplication. This is tough for me since the mapping from R x S to S x R could be anything! How can I even start if I don't have this function or mapping?