Find which of the operations given above has identity.

Open in App

Solution

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

a * e = a = e * a, a ∈ Q.

However, there is no such element e ∈ Q with respect to each of the six operations satisfying the above condition.

Thus, none of the six operations has identity.

Suggest Corrections

Similar questions

Find which of the operations given above has identity.

Q. Which among the following operation/s has/have 0 as an identity element?

Let $*$ be a binary operation on the set Q of rational number as follows:
$(v i) a * b = a b^{2}$
Show that none of the operations has an identity.

Let $*$ be a binary operation on the set Q of rational number as follows:
$(i) a * b = \frac{a b}{4}$
Show that none of the operations has an identity.

Let $*$ be a binary operation on the set Q of rational number as follows:
$(i i i) a * b = a + a b$
Show that none of the operations has an identity.

Join BYJU'S Learning Program

Find which of the operations given above has identity.

An element e ∈ Q will be the identity element for the operation * if a * e = a = e * a, a ∈ Q. However, there is no such element e ∈ Q with respect to each of the six operations satisfying the above condition. Thus, none of the six operations has identity.

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

a * e = a = e * a, a ∈ Q.

However, there is no such element e ∈ Q with respect to each of the six operations satisfying the above condition.

Thus, none of the six operations has identity.