Let $B \in M_3(\mathbb{R})$ be antisymmetric. Show that there exist a matrix $P$ of $O_3(\mathbb{R})$ and a real number $\beta$ such that $$B = P \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & -\beta \\ 0 & \beta & 0 \end{pmatrix} P^{-1}$$
Let $B \in M_3(\mathbb{R})$ be antisymmetric.
Show that there exist a matrix $P$ of $O_3(\mathbb{R})$ and a real number $\beta$ such that
$$B = P \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & -\beta \\ 0 & \beta & 0 \end{pmatrix} P^{-1}$$