let $R$ be a ring, if every element $x$ satisfies $x^3=x$ then show that $R$ is commutative.
Yes, I have read the other two posts regarding this question, and saw many many solutions, however none seems to explain how they arrive at the solution?
Can someone care to show me some advice on how might one arrive at a solution for these problem? Not just the proof itself but how it could have been deduced?
Or is this one of those problems you just have to try different things until you lead to something that works?
thank you
