Let * be a binary operation defined on $Q^{+}$(the set of positive rational numbers) by the rule $a * b=\frac{a b}{7}$ for all $a, b \in Q^{+}$. Then inverse of $2$ is:

$\frac{49}{2}$

The correct answer is Option (3) - $\frac{49}{2}$

let e be identity

so $a*e=a$

$⇒\frac{ae}{7}=a⇒e=7$

so $a*a^{-1}=e⇒\frac{aa^{-1}}{7}=7⇒a^{-1}=\frac{49}{a}$

so inverse of 2 is $\frac{49}{2}$