Definition: Identity property

The identity property refers to the property of an operation where a specific element exists within a set, such that combining any element of the set with this specific element using the operation results in the original element itself.

There are two main types of identity properties in algebra:

Explanation:

Additive Identity Property: This property states that when any number is added to zero, the result is the original number itself. In other words, the sum of any number and zero is that number. Symbolically, it can be expressed as a + 0 = a.

Where a is any number and 0 is called the additive identity element.

Multiplicative Identity Property: This property states that when any number is multiplied by one, the result is the original number itself. In other words, the product of any number and one is that number. Symbolically, it can be expressed as \$a times 1 = a\$.

Where a is any number and 1 is called the multiplicative identity element.