A binary operation is *commutative* if *ab* = *ba* for ALL
possible *a* and *b* in the set. Addition and multiplication in the reals are
commutative operations whereas multiplication of matrices generally is not.

Note that the definition requires *ab*=*ba* for all pairs of elements. That
some element commutes with all elements does not make the operation
commutative.

For a finite set whose binary operation is given in a table, it is easy to observe whether the operation is commutative. If we write the elements along the rows in the same order as down the column then if the table is symmetric about the diagonal then it is commutative.

Tue Dec 3 14:15:35 PST 1996