What is the identity property in math?

Answer 1

The identity property exists only in the context of a set (such as integers or rationals or reals) AND a binary operator (such as multiplication or addition).

The identity property of a set with the binary operation # states that there is a unique element in the set, called the identity which is denoted by i, such that

x # i = i # x = x for all elements x is the set.

In the sets mentioned above,

the additive identity is 0;

the multiplicative identity is 1.