Two numbers, x and z, are said to be commutative under addition if

 

    x + y = y + x

 

and to be commutative under multiplication if

 

    x × y = xy × yx

 

In general, two elements a and b of a set S are commutative under the binary operation (an operation that works on two elements at a time) * if

 

    a * b = ab * ba

 

Compare with associative and distributive.