Exercise on real numbers [closed]

Let $A$ be the set of real numbers defined by :

$$A = \left\{nm+\frac{1}{nm} \; \middle|\; n \in \mathbf{N}^*, m\in \mathbf{N}^* \right\}$$

1. Show that : $\max(A) = 2$.

2. Show that : $\inf(A) = 1$.

3. Deduce from the previous questions that $A$ has no minimum.