Problem:
Prove that the commutativity on the set of non-scalar $2\times2$ matrices is an equivalence relation. (That is, for all A; B; and C; if AB = BA and BC = CB then AC = CA:)
For commutativity to be equivalence relation, we have to it is reflexive, symmetric and transitive. The first two properties are obvious. Any help on how to prove the third property?