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

To solve the problem, we need to find the identity element for the binary operation defined on the set of rational numbers \( Q \) and prove that every non-zero element of \( Q \) is invertible.

### Step 1: Define the Binary Operation
The binary operation \( * \) is defined as:
\[ a * b = \frac{ab}{5} \]
for all \( a, b \in Q \).
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