On Q the set of all rational numbers, a binary operation $\ast$ is defined by $a \ast b=\frac{ab}{5}$ for all $a, b \in Q $. Find the identity element $\ast$ in Q. Also prove that every non-zero element of Q is invertible.

Question

$(A)\; \frac{26}{a}$
$(B)\; -\frac{26}{a}$
$(C)\; \frac{25}{a}$
$(D)\; -\frac{25}{a}$