Find if the given below operation has identity?

(iii) $a * b = a + a b$

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Solution

Given: $a * b = a + a b$

$e$ is the identity of $$ if

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

There is no possible value of $e$ where,

$a + a e = e + a e = a$

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

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Q

a * b = a + a b

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