To determine which property is illustrated by the equation [tex]\( a \times 1 = a \)[/tex], let's examine the properties of multiplication one by one:
1. Identity Property of 1:
- This property states that any number multiplied by 1 remains unchanged. In symbolic form: [tex]\( a \times 1 = a \)[/tex].
2. Inverse Property of Multiplication:
- This property states that each number has a multiplicative inverse such that multiplying the number by its inverse yields the identity (which is 1). In symbolic form: [tex]\( a \times \frac{1}{a} = 1 \)[/tex] (assuming [tex]\( a \neq 0 \)[/tex]).
3. Commutative Property of Multiplication:
- This property states that the order of the numbers does not affect the product. In symbolic form: [tex]\( a \times b = b \times a \)[/tex].
4. Associative Property of Multiplication:
- This property states that the way in which numbers are grouped in multiplication does not affect the product. In symbolic form: [tex]\((a \times b) \times c = a \times (b \times c)\)[/tex].
Now, let's see which property matches the given equation [tex]\( a \times 1 = a \)[/tex].
- The equation [tex]\( a \times 1 = a \)[/tex] exactly matches the Identity Property of 1 because it demonstrates that when any number [tex]\( a \)[/tex] is multiplied by 1, the product is the number [tex]\( a \)[/tex] itself.
Therefore, the correct answer is:
Identity Property of 1
