Let mathbb Q ^+ be the set of positive rational numbers with operation a * b = frac ab 2 . What is the identity element e such that a * e = a for all a in mathbb Q ^+?

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SSC Pure Mathematics QUESTION #4109

Question 1

Let $\mathbb{Q}^+$ be the set of positive rational numbers with operation $a * b = \frac{ab}{2}$. What is the identity element $e$ such that $a * e = a$ for all $a \in \mathbb{Q}^+$?

$e = 0$
$e = 1$
$e = 2$✔️
$e = \frac{1}{2}$

Correct Answer Explanation

For identity: $a * e = \frac{ae}{2} = a$, so $ae = 2a$, thus $e = 2$.

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