The identity element for the binary operation $*$ if $a*b = \dfrac{ab}{4}, \forall a, b \in Q$

The correct answer is 4

Given $a*b = \dfrac{ab}{4}$

We know that $a*e$ = $a$ = $e*a$

⇒ $\dfrac{ae}{4}$ = $a$ = $\dfrac{ea}{4}$

∴ To satisfy the above equation, $e$ should be $4$