`Q^+` denote the set of all positive rational numbers. If the binary operation `o.` on `Q^+` is defined as a `o.b=(a b)/2,` then the inverse of 3 is `4/3` (b) 2 (c) `1/3` (d) `2/3`

Explanation

`frac{4}{3}`

Let e be the identity element in `Q^{+}`with respect to` odot `such that
`

a * e=a=e * a, forall a in Q^{+} `
`
a * e=a text { and } e * a=a, forall a in Q^{+} `
`
frac{a e}{2}=a text { and } frac{e a}{2}=a, forall a in Q^{+} `
`
e=2, forall a in Q^{+}`


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