How do you prove a Ring to be commutative?

Answer 1

To prove a ring is commutative, one must show that for any two elements of the ring their product does not depend on the order in which you multiply them. For example, if p and q are any two elements of your ring then p*q must equal q*p in order for the ring to be commutative.

Note that not every ring is commutative, in some rings p*q does not equal q*p for arbitrary q and p (for example, the ring of 2x2 matrices).