Determine whether the following elements of $\operatorname{PSL}_{2}(\mathbb{R})$ are elliptic, parabolic, or hyperbolic. Justify your answers.

$$\left(\begin{array}{cc} 5 & 8 \\ -2 & -3 \end{array}\right), \quad\left(\begin{array}{cc} -3 & 1 \\ 2 & -1 \end{array}\right)$$

In the case of the first of these transformations find the fixed points.