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

Correct answer: (0)

Step 1: For identity (e), we need (a*e=a). Step 2: (a+e-ae=a\Rightarrow e(1-a)=0), so (e=0) works for every (a\in A). Step 3: In exams, always verify both (a*e=a) and (e*a=a).