The Identity Property refers to operations that leave an element unchanged. There are two main identity properties:

1. Additive Identity Property: This property states that adding zero to any number does not change the number. Zero is the "identity" for addition.

   • $a + 0 = a$
   • Example: $7 + 0 = 7$

2. Multiplicative Identity Property: This property states that multiplying any number by one does not change the number. One is the "identity" for multiplication.

   • $a \times 1 = a$
   • Example: $5 \times 1 = 5$

These properties are called "identity" because the number retains its identity (value) after the operation.

Follow-up Questions:

1. Do you need an example that involves both the identity and inverse properties?
2. Are you curious about how these identity properties are used in algebraic equations?
3. Would you like to know how identity properties relate to other mathematical operations?
4. Do you want to explore how the identity property works with matrices or other advanced topics?
5. Are there any other properties you'd like to review, such as associative or commutative?

Tip: Remember, identity properties are fundamental in simplifying expressions and solving equations. They help in recognizing when a number remains unchanged after an operation.