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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 R0 of all non-zero real numbers by the rule $\text{a}\times\text{b}=\frac{\text{ab}}{2}$ for all a, b ∈ R0.
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Answer

 $\because\ \text{a}\times\text{b}=\frac{\text{ab}}{2}$ for all a, b ∈ R0

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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