Show that none of the operations given above has an identity element.

(N/A) An element $e \in Q$ is the identity element for a binary operation $^*$ if $a * e = a = e * a$ for all $a \in Q$.
For the six operations typically defined on the set of rational numbers $Q$ (such as $a * b = a + b + ab$,$a * b = a - b$,etc.),we test the condition $a * e = a$.
If we solve $a * e = a$ for each operation,we find that the resulting value of $e$ depends on $a$ or does not exist within the set $Q$ for all $a$.
Since there is no single element $e \in Q$ that satisfies the condition $a * e = a = e * a$ for all $a \in Q$ across these operations,none of the operations has an identity element.