5. Let $L_{e_1}$ and $R_\theta$ be defined as in Problem 4, and let $f, g: \mathbb{R}^2 \to \mathbb{R}^2$ be the isometries defined by
$f = L_{e_1} \circ R_\pi$ and $g = R_{\frac{\pi}{2}} \circ L_{e_1} \circ T_{(2, -1)}$
(a) Express $f \circ g$ in the form
$f \circ g = T_z \circ R_\theta$,
where $z \in \mathbb{R}^2$ and $\theta \in \mathbb{R}$.
(b) Express $g \circ f$ in the form
$g \circ f = T_y \circ R_\psi$,
where $y \in \mathbb{R}^2$ and $\psi \in \mathbb{R}$.
