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Binary Operations — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSBinary Operations2 Marks
Question
Write the identity element for the binary operation $*$ on the set $R_0$ of all non$-$zero real numbers by the rule $\text{a}\times\text{b}=\frac{\text{ab}}{2}$ for all $a, b \in R_0.$
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Answer

$\because\ \text{a}\times\text{b}=\frac{\text{ab}}{2}$ for all $a, b \in R_0$
Let e be the identity element, then
$a * e = a$
$\Rightarrow\frac{\text{ae}}{2}=\text{a}$
$\Rightarrow\text{e}=2$
Thus, $e = 2$ is the identity element with respect to $*.$

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