Question

The identity element for the binary operation * defined on Q ~ {0} as a * b = `"ab"/2` ∀ a, b ∈ Q ~ {0} is ______.

Options

• 1

• 0

• 2

• none of these

Answer 1

The identity element for the binary operation * defined on Q ~ {0} as a * b = `"ab"/2` ∀ a, b ∈ Q ~ {0} is 2.

Explanation:

Given that, a * b = `"ab"/2` ∀ a, b ∈ Q ~ {0} 

Let e be the identify element for *

∴ a * e = `"ae"/2`

⇒ a = `"ae"/2`

⇒ e = 2