On (A={1,2,3,4,5,6}), (a*b=\gcd(a,b)) is defined. What is the correct statement about the inverse of (4), if identity is assumed to be (6)?

Correct answer: It has no inverse

Step 1: For inverse (x), we need (\gcd(4,x)=6). Step 2: For any (x\in A), (\gcd(4,x)) can be at most (4), so it cannot be (6). Step 3: An inverse exists only if the operation can reach the identity element.