Mathematics Question from JEE Main 2023 · 30 January, Shift 2

Let $A = \{ 1, 2, 3, 5, 8, 9 \}$. Then the number of possible functions $f : A \to A$ 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 _____