Consider the following statements:

1. If $x$ is directly proportional to $z$ and $y$ is directly proportional to $z$, then $\left(x^2-y^2\right)$ is directly proportional to $z^2$.
2. If $x$ is inversely proportional to $z$ and $y$ is inversely proportional to $z$, then $\left(xy\right)$ is inversely proportional to $z^2$.

Which of the above statements is/are correct?