Question

Let $A=\\{1,2,3,5,8,9\\}$ Then the number of possible functions $f: A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to______

Answer 1

f(1)=1;f(9)=f(3)×f(3)
i.e., f(3)=1 or 3
Total function =1×6×2×6×6×1=432
So, the correct answer is 432.