What is the Identity Property?

Identity Property is a fundamental concept in mathematics that applies to arithmetic operations. It is defined as the property where if any arithmetic operations are used to combine an identity with a number (n), the end result will be n.

In simple words, when you add, subtract, multiply, or divide a number by a specific value, there’s a special number that won’t change the result. That special number is the Identity Element for the defined operation.

The identity property is applied to a group of numbers in the form of sets, and the identity of these numbers remains the same as 1 and 0 even when the numbers are added, subtracted, multiplied, and divided.

Identity Property Definition

For any number a and operation ” * “, identity property is defined as:

a * e = e * a = a

Where e is the identity element under operation ” * “.

Condition for Identity Property to Not Hold

Consider the set of real numbers. The operation we’re considering here is exponentiation, denoted by ^. According to the Identity Property of Exponentiation, for any real numbera, a^e = e^a = a.

As we know, for any two real number it only holds true if both a and e are 1, other than that this relation doesn’t hold true for any real number.

Thus, identity property doesn’t hold for real numbers under the operation of exponentiation i.e., a^e ≠ e^a.

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.