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Binary Operations — Maths STD 12 Science — Question

Gujarat 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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