Question

The identity element for the binary operation * defined on Q - {0} as: a * b = \(\rm \frac{ab}{2}\), is:

Answer 1

Correct Answer - Option 3 : 2

Concept:

An identity element is a special type of element of a set with respect to a binary operation on that set, which leaves any element of the set unchanged when combined with it.

 

Calculation:

It is given that a * b = \(\rm \frac{ab}{2}\); a,b ∈ Q - {0}.

Let the identity element for * be i, i.e. a * i = a.

∴ a * i = \(\rm \frac{ai}{2}\)

⇒ a = \(\rm \frac{ai}{2}\)

⇒ i = 2.

Hence, the identity element for the operation * is i = 2.