What is the definition for identity property of multiplication?

Answer 1

The identity property for a set with the operation of multiplication defined on it is that the set contains a unique element, denoted by i, such that for every element x in the set,

i * x = x = x * i

The set need not consist of numbers, and the multiplication need not be the everyday kind of multiplication. Matrix multiplication is an example.

Answer 2

A set S is said to have a multiplicative identity if the set contains an element - usually denoted by 1) such that for all elements x , in S,

x*1 = x = 1*x