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# The identity element of the binary operation $\large *$ defined on $Q-\{0\}$ as $a\large *$ $b=\large\frac{ab}{2},$ $\forall \:a,b\:\in\:Q-\{0\}$

(A) 0

(B) 1

(C) 2

(D) Does not exists

Can you answer this question?

Let $e\in\:Q-\{0\}$ be the identity element of $\large *$
According to definition of identity element $a\large *$ $e=a$
Given: $a\large *$ $b=\large\frac{ab}{2}$
$\Rightarrow\:\:a\large *$ $e=\large\frac{ae}{2}$ $=a$
$\Rightarrow\:\:e=2$
answered May 31, 2013