- In arithmetic, multiplication of one number, a, by another, b, consists of adding a to itself b times. This kind of multiplication is commutative, i.e. . The identity element for arithmetic multiplication is 1, i.e. multiplication by 1 produces no change. In a series of multiplications the order in which they are carried out makes no difference to the result. For example, . This is the associative law for arithmetic multiplication. Multiplication of vectors and matrices do not follow the above rules.