# The identity element of the binary operation $\large *$ defined on $Q-\{0\}$ as $a\large *$ $b=\large\frac{ab}{2},$ $\forall \:a,b\:\in\:Q-\{0\}$

(A) 0

(B) 1

(C) 2

(D) Does not exists

Let $e\in\:Q-\{0\}$ be the identity element of $\large *$
According to definition of identity element $a\large *$ $e=a$
Given: $a\large *$ $b=\large\frac{ab}{2}$
$\Rightarrow\:\:a\large *$ $e=\large\frac{ae}{2}$ $=a$
$\Rightarrow\:\:e=2$