In this section, the dimension of $E$ is 8. Show that, for all $(x_{0}, \ldots, x_{7}) \in \mathbb{R}^{8}$,
$$\left(\begin{array}{cccccccc}
x_{0} & -x_{1} & -x_{2} & -x_{4} & -x_{3} & -x_{5} & -x_{6} & -x_{7} \\
x_{1} & x_{0} & -x_{4} & x_{2} & -x_{5} & x_{3} & -x_{7} & x_{6} \\
x_{2} & x_{4} & x_{0} & -x_{1} & -x_{6} & x_{7} & x_{3} & -x_{5} \\
x_{4} & -x_{2} & x_{1} & x_{0} & x_{7} & x_{6} & -x_{5} & -x_{3} \\
x_{3} & x_{5} & x_{6} & -x_{7} & x_{0} & -x_{1} & -x_{2} & x_{4} \\
x_{5} & -x_{3} & -x_{7} & -x_{6} & x_{1} & x_{0} & x_{4} & x_{2} \\
x_{6} & x_{7} & -x_{3} & x_{5} & x_{2} & -x_{4} & x_{0} & -x_{1} \\
x_{7} & -x_{6} & x_{5} & x_{3} & -x_{4} & -x_{2} & x_{1} & x_{0}
\end{array}\right)$$
is a similarity matrix. What can we deduce from this?