Multiplicative inverse of `(0)/(1)` is

Options

A. 1
B. `-1`
C. 0
D. not defined

Answer

To find the multiplicative inverse of the rational number \( \frac{0}{1} \), we can follow these steps:

### Step 1: Understand the concept of multiplicative inverse
The multiplicative inverse of a number \( x \) is a number \( y \) such that when \( x \) is multiplied by \( y \), the result is \( 1 \). In mathematical terms, \( x \times y = 1 \).

### Step 2: Identify the number
In this case, the number we are considering is \( \frac{0}{1} \), which is simply \( 0 \).

### Step 3: Determine the multiplicative inverse of 0
To find the multiplicative inverse of \( 0 \), we need to find a number \( y \) such that:
\[ 0 \times y = 1 \]
However, any number multiplied by \( 0 \) will always equal \( 0 \), not \( 1 \). Therefore, there is no number \( y \) that can satisfy this equation.

### Step 4: Conclusion
Since there is no number that can be multiplied by \( 0 \) to yield \( 1 \), we conclude that the multiplicative inverse of \( \frac{0}{1} \) (or \( 0 \)) is undefined.

### Final Answer
The multiplicative inverse of \( \frac{0}{1} \) is **undefined**.

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