PROBLEM 2. Let the set $A=\left\{n \mid n=2^{a} \cdot 3^{b} \cdot 5^{c}\right.$, where $\left.a, b, c \in \mathbb{N}\right\}$.

a) Show that $81 \in A$;

b) Determine the elements of the set $A$ that have exactly 6 divisors.