Find if the given below operation has identity?

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

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Solution

Given: $a * b = \frac{a b}{4}$

$e$ is the identity of $$ if

$a e = e * a = a i . e ., \frac{a e}{4} = \frac{e a}{4} = a,$

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

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Q

a * b = \frac{a b}{4}

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