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Binary Operations — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsBinary Operations2 Marks
Question
Let 'o' be a binary operation on the set $Q_0$​​​​​​​ of all non-zero rational numbers defined by $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{2} $ for all $\text{a},\text{b}\in\text{Q}_0.$
Find the identity element in $Q_0$​​​​​​​.
✓

Answer

We have,
$a ^* b=\frac{ ab }{2}$ for all $a , b \in Q _0$
Let $e \in Q _0$ be the identity element with respect to *.
By identity property, we have,
$a^* e=e^* a=a \text { for all } a \in Q_0$
$\Rightarrow \frac{ae}{2}=a \Rightarrow e=2$
Thus the required identity element is $2$ .

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