Question

Find if the given below operation has identity?

(v) $a\ast b=\frac{ab}{4}$

Answer 1

Given: $a\ast b=\frac{ab}{4}$

$e$ is the identity of $\ast$ if

$a\ast e=e\ast a=ai.e.,\frac{ae}{4}=\frac{ea}{4}=a,$

It is possible if $e=4$
So, $4$ is the identity element in $\ast .$