On the set (A={0,1,2,3}), (a*b) is defined as the remainder obtained when (a+b) is divided by (4). What is the inverse of (3)?

Correct answer: (1)

Step 1: Adding (0) leaves every element unchanged, so the identity is (0). Step 2: (3*x=0) means (3+x) must have remainder (0) on division by (4). With (x=1), the sum is (4). Step 3: In remainder operations, the inverse makes the sum a multiple of the modulus.