What is the meaning of idenaty property?

Answer 1

The identity element of a set S, with respect to a binary operation ~ is an element of S, denoted by i such that, for every element x, of S,

x~i = i~x = x

With the "normal" sets of numbers, if the operation is addition, then the identity element is 0, and the identity property is x + 0 = 0 + x = x

If the operation is multiplication, the identity element is 1, and the identity property is x * 1 = 1 * x = x.

Answer 2

It means that there is a certain element which, when used in an operation, doesn't change the result. For example, if you add any number "x" with 0 (0 is the identity element for addition), you get back the original result, i.e., "x".