On Q, the set of all rational numbers, a binary operation * is defined by `a*b=(a b)/5` for all `a , b in Qdot` Find the identity element for * in Q. Also, prove that every non-zero element of Q is invertible.

Explanation

Here, `a**b = (ab)/5`.

An identity element `e` in a relation is an element such that

`a**e = e**a = a.`

So, in the given relation,

`a**e = (ae)/5 = a => ae = 5a => e = 5`

So, identity element is `5` for the given relation.

Now, for any element `x in Q`,

If `a**x = e`, then `x` is inverse of `a`.

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