Find if the given below operation has identity?

(i) $a * b = a - b$

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Solution

Given: $a * b = a - b$

$e$ is the identity of $$ if

$a e = e * a = a i . e ., a - e = e - a = a$

There is no possible value of $e$ where,

$a - e = e - a$

So, $*$ has no identity element in $Q .$

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Q

a * b = a - b

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