Write the identity element for the binary operation * on the set … - Vidyadip

Question

Write the identity element for the binary operation * on the set $R _0$ of all non-zero real numbers by the rule $a \times b=\frac{a b}{2}$ for all $a, b \in R_0$.

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Answer

$\because a \times b =\frac{ ab }{2}$ for $all a , b \in R _0$ Let e be the identity element, then
$a^* e=a$
$\Rightarrow \frac{ ae }{2}= a \Rightarrow e =2$
Thus, $e =2$ is the identity element with respect to *.

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