Show that none of the operations given above has identity.
Show that none of the operations given above has identity.
An element $e$ $\in Q$ will be the identity element for the operation $^*$
if $a^{*} e=a=e^{*}$ $a$, for all $a \in Q$
However, there is no such element $e \in Q$ with respect to each of the six operations satisfying the above condition.
Thus, none of the six operations has identity.
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