COMMUTATIVE LAW

in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + b = b + a and ab = ba; that is, a finite sum or product is unaltered by reordering the terms or factors. While commutativity holds for many systems, there are exceptionsas in quaternions in which commutativity of multiplication is invalid. Scalar multiplication of two vectors (to give the so-called dot product) is commutative (i.e., ab = ba), but vector multiplication (to give the cross product) is not (i.e., a b = -b a). The commutative law does not necessarily hold for multiplication of conditionally convergent series. See also associative law; distributive law.