Let * be a binary operation on set `Q-[1]` defined by `a*b=a+b-a b` for all`a , b in Q-[1]dot` Find the identity element with respect to `*onQdot` Also, prove that every element of `Q-[1]` is invertible.

Explanation

To solve the problem, we need to find the identity element with respect to the binary operation defined by \( a * b = a + b - ab \) for all \( a, b \in \mathbb{Q} - \{1\} \). We also need to prove that every element in \( \mathbb{Q} - \{1\} \) is invertible.

### Step 1: Find the Identity Element

1. **Definition of Identity Element**: An identity element \( e \) for the operation \( * \) must satisfy the condition \( a * e = a \) for all \( a \in \mathbb{Q} - \{1\} \).

2. **Set Up the Equation**: Using the definition of the operation, we have:
\[
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