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Question
Let 'o' be a binary operation on the set Q0 of all non-zero rational numbers defined by \[a o b = \frac{ab}{2}, \text{ for all a, b } \in Q_0\] :
Find the identity element in Q0.
Solution
Let e be the identity element in Qo with respect to * such that
\[a o e = a = e o a, \forall a \in Q_0 \]
\[a o e = a \text{ and }e o a = a, \forall a \in Q_0 \]
\[ \Rightarrow \frac{ae}{2} = a \text{ and }\frac{ea}{2} = a, \forall a \in Q_0 \]
\[e = 2 \in Q_0 , \forall a \in Q_0\]
Thus, 2 is the identity element in Qo with respect to o.
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