Consider the set Q with binary operation `'**'` as:
`a**b=(ab)/(4)`. Then, the identity element is:

Options

A. `(1)/(4)`
B. 1
C. 4
D. 16

Answer

To find the identity element for the binary operation defined on the set Q, we follow these steps:

1. **Understanding the Binary Operation**: We are given a binary operation defined as \( a ** b = \frac{ab}{4} \).

2. **Definition of Identity Element**: An identity element \( e \) for this operation must satisfy the condition that for any element \( a \) in the set Q, the following holds:
\[ a ** e = a \quad \text{and} \quad e ** a = a \]

3. **Calculating \( a ** e \)**: Using the operation definition, we have:
\[ a ** e = \frac{ae}{4} \]
For \( e \) to be the identity element, we need:
\[ \frac{ae}{4} = a \]

4. **Solving for \( e \)**: We can rearrange the equation:
\[ ae = 4a \]
Assuming \( a \neq 0 \) (since we are looking for a general identity element), we can divide both sides by \( a \):
\[ e = 4 \]

5. **Calculating \( e ** a \)**: We also need to check the other condition:
\[ e ** a = \frac{ea}{4} \]
Substituting \( e = 4 \):
\[ 4 ** a = \frac{4a}{4} = a \]

6. **Conclusion**: Since both conditions \( a ** e = a \) and \( e ** a = a \) are satisfied, we conclude that the identity element is:
\[ e = 4 \]

### Final Answer:
The identity element is \( 4 \).

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