Types of Identity Properties

There are two main types of Identity Properties:

• Identity Property of Addition
• Identity Property of Multiplication

Identity Property of Addition

For addition, the identity element is usually denoted as 0. The Identity Property of Addition states that for any element a in the set, a + 0 = 0 + a = a.

For example, 7 + 0 = 0 + 7 = 7 and −1 + 0 = 0 + (-1) = −1.

In both cases, adding 0 to a does not change the value of a, illustrating the Identity Property of Addition.

Note: 0 is the additive identity i.e., identity element for addition operation.

Identity Property of Multiplication

For multiplication, the identity element is typically denoted as 11. The Identity Property of Multiplication states that for any element a in the set, a × 1 = 1 × a = a.

For example, 5 × 1 = 1 × 5 = 5 and −2 × 1 = 1 × (-2) =−2.

In each case, multiplying a by 1 yields a, demonstrating the Identity Property of Multiplication.

Note: 1 is the multiplicative identity i.e., identity element for multiplication operation.

Identity Property, also known as the Identity Element or Identity Law, is a fundamental concept in mathematics. It is used primarily in the study of groups, rings or fields in abstract algebra.

Identity Property ensures that there exists a special element within a set that leaves other elements unchanged when combined with them using a defined operation. In this article, we will discuss Identity Property in detail including its definition. We will also discuss the Identity Property of addition and multiplication as well.