Consider the following permutations $f, g$, and $h$ in $S_{6}$ :
$$
\begin{gathered}
f=\left(\begin{array}{llllll}
1 & 2 & 3 & 4 & 5 & 6 \\
6 & 1 & 3 & 5 & 4 & 2
\end{array}\right) \quad g=\left(\begin{array}{llllll}
1 & 2 & 3 & 4 & 5 & 6 \\
2 & 3 & 1 & 6 & 5 & 4
\end{array}\right) \\
h=\left(\begin{array}{llllll}
1 & 2 & 3 & 4 & 5 & 6 \\
5 & 1 & 6 & 4 & 5 & 2
\end{array}\right)
\end{gathered}
$$
Compute the following:
$f^{-1}=\left(\begin{array}{cccccc}1 & 2 & 3 & 4 & 5 & 6 \\ & & & & & \end{array}\right) \quad g^{-1}=\left(\begin{array}{cccccc}1 & 2 & 3 & 4 & 5 & 6 \\ & & & & & \end{array}\right)$
$h^{-1}=\left(\begin{array}{llllll}1 & 2 & 3 & 4 & 5 & 6 \\ & & & & & \end{array}\right)$
$f \circ g=\left(\begin{array}{cccccc}1 & 2 & 3 & 4 & 5 & 6 \\ \vdots & & & & \end{array}\right) \quad g \circ f=\left(\begin{array}{llllll}1 & 2 & 3 & 4 & 5 & 6\end{array}\right)$