Question

Find if the given below operation has identity?

(i) $a\ast b=a-b$

Answer 1

Given: $a\ast b=a-b$

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

$a\ast e=e\ast a=ai.e.,a-e=e-a=a$

There is no possible value of $e$ where,

$a-e=e-a$

So, $\ast$ has no identity element in $Q.$