On (A={0,1,2}), (a*b) is the remainder obtained when (ab) is divided by (3). What is the inverse of (2)?

Correct answer: (2)

Step 1: In this multiplication-based remainder operation, the identity is (1). Step 2: We need (2*b=1). Since (2\cdot2=4), and the remainder of (4) on division by (3) is (1), the inverse is (2). Step 3: While finding an inverse, always equate the operation result to the identity element.