Question

Find which of the operations given above has identity.

Answer 1

An element e ∈ Q will be the identity element for the operation * if

a * e = a = e * a, ∀ a ∈ Q.

We are given

a * b = ab4

⇒ a*e = a⇒ae4=a⇒ e=4

Similarly, it can be checked for e*a=a, we get e=4 Thus, e = 4 is the identity