Let S be the set of all rational numbers except 1 and * be defined on S by `a*b=a+b-a b ,` for all`a , b in Sdot` Find its identity element

Explanation

To find the identity element of the binary operation defined on the set \( S \) of all rational numbers except 1, we need to follow these steps:

### Step 1: Define the operation and the identity element
Let the operation \( * \) be defined as:
\[ a * b = a + b - ab \]
for all \( a, b \in S \). We want to find an identity element \( E \) such that:
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