On (A=\mathbb{R}\setminus{1}), (a*b=a+b-ab) is defined. Choose the correct statement about this operation on this set.

Correct answer: It is closed

Step 1: (1-(a*b)=1-a-b+ab=(1-a)(1-b)). Step 2: If (a\neq 1) and (b\neq 1), then ((1-a)(1-b)\neq 0), so (a*b\neq 1). Step 3: To check closure on an excluded-value set, show that the excluded value cannot appear as an output.