Question

The identity element for the binary operation * defined by a * b = $\frac{ab}{2}$, $a,b \in Q_{0}$ (the set of all non-zero rational numbers) is

• A. 1
• B. 0
• C. 2
• D. None of these

Answer 1

Answer: (C)

2

Answer 2

Let e be the identity element for the binary operation * on $Q_{0}$defined by $a*b = \frac{ab}{2}$

Then, $a*e = a = e*a$ for all $a \in Q_{0}$

⇒ $\frac{ae}{2} = a$ for all $a \in Q_{0}$ ⇒ $e = 2$