Find which of the operations given above has identity.

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Solution

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 = $\frac{a b}{4}$

$\Rightarrow a * e = a \Rightarrow \frac{a e}{4} = a \Rightarrow e = 4 Similarly, it can be checked for e * a = a, we get e = 4 Thus, e = 4 is the identity .$

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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. We are given a * b = ab4 ⇒ a*e = a⇒ae4=a⇒ e=4Similarly, it can be checked for e*a=a, we get e=4Thus, e = 4 is the identity.

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 = $\frac{a b}{4}$

$\Rightarrow a * e = a \Rightarrow \frac{a e}{4} = a \Rightarrow e = 4 Similarly, it can be checked for e * a = a, we get e = 4 Thus, e = 4 is the identity .$