The identity element for the binary operation $*$ defined on $\mathbb{Q} - \{0\}$ as $a * b = \frac{ab}{2}, \forall a, b \in \mathbb{Q} - \{0\}$ is

2

The correct answer is Option (3) → 2 ##

Given that, $a * b = \frac{ab}{2}, \forall a, b \in \mathbb{Q} - \{0\}$.

Let $e$ be the identity element for $*$.

$∴a * e = \frac{ae}{2} \quad [∵a * e = e * a = a]$

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