On the set (\mathbb{R}\setminus{-1}), the operation (a*b=a+b+ab) is defined. What is the identity element for this operation?

Correct answer: (0)

Step 1: For identity (e), we need (a*e=a). Step 2: From (a+e+ae=a), we get (e(1+a)=0). Since (a\neq -1), (e=0). Step 3: In identity questions, always apply the condition with a general element.