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# Let * ba a binary operation on set Q of rational defined as $a*b=\large\frac{ab}{5}.$ Write the identity for * , if any.

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• An element $e \in N$ is an identify element for operation * if $a*e=e*a$ for all $a \in N$
Let $e$ be the identity element in $Q^+$.
Then $a\ast e=e\ast a$ for all $a\in Q^+$
$\Rightarrow \large\frac{ae}{5}$$=a and \large\frac{ae}{5}$$=a$ forall $a\in Q^+$
$\Rightarrow e=5$
Hence $5$ is the identity element in $Q^+$
answered Oct 1, 2013