What is the multiplicative identity element in the set of whole numbers?

Options

A. 0
B. `-1`
C. 1
D. 2

Answer

To find the multiplicative identity element in the set of whole numbers, we can follow these steps:

### Step 1: Understand the definition of multiplicative identity
The multiplicative identity is a number that, when multiplied by any number in a given set, leaves that number unchanged.

**Hint:** Think about what happens when you multiply a number by 1.

### Step 2: Identify the set of whole numbers
Whole numbers are defined as the set of non-negative integers: {0, 1, 2, 3, ...}.

**Hint:** Remember that whole numbers start from 0 and go on indefinitely.

### Step 3: Test the multiplicative identity
To find the multiplicative identity, we need to find a number \( B \) such that for any whole number \( A \):
\[ A \times B = A \]

**Hint:** Consider what number you can multiply with any whole number that will not change its value.

### Step 4: Substitute the value of B
If we let \( B = 1 \), we can check:
\[ A \times 1 = A \]
This holds true for any whole number \( A \).

**Hint:** Try substituting different whole numbers to see if the result remains the same when multiplied by 1.

### Step 5: Conclusion
Since multiplying any whole number by 1 gives the same whole number, we conclude that the multiplicative identity element in the set of whole numbers is:
**1**

**Final Answer:** The multiplicative identity element in the set of whole numbers is **1**.