Question

The identity element for the binary operation $\ast$ defined on $Q-\left\{0\right\}$ as

$a\ast b=\frac{ab}{2}\forall a,b\in Q-\left\{0\right\}$ is

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

Answer 1

The correct option is A $2$

Find identity element

Given: $a\ast b=\frac{ab}{2}\forall a,b\in Q\sim \left\{0\right\}$

Let $e$ be the identity element

$\therefore a\ast e=a=e\ast a$

$\Rightarrow a\ast e=\frac{ae}{2}=a$

$\Rightarrow e=2$

Hence, the correct answer is (c).