Rotation Matrices

So I recently took interest in having fun with rotation matrices by analyzing two vectors, their inner products, their cross products, and their bisecting vectors after my previous post. Basically, the rotation matrices I am interested in are:
$$
\mathbf{R}^{3}_{\hat{n}}\left(\pm\frac{\pi}{2}\right)=

\begin{pmatrix}
0 & \mp 1 & 0 \\
\pm 1 & 0 & 0\\
0 & 0 & 1
\end{pmatrix}\\
\mathbf{R}^{3}_{\parallel}\left(\pm\frac{\pi}{2}\right)=

\begin{pmatrix}
1 & 0 & 0 \\
0 & 0 & \mp 1\\
0 & \pm 1 & 0
\end{pmatrix}\\

\mathbf{R}^{3}_{\perp}\left(\pm\frac{\pi}{2}\right)=

\begin{pmatrix}
0 & 0 & \pm 1 \\
0 & 1 & 0\\
\mp 1 & 0 & 0
\end{pmatrix}


$$
I'ts kinda late, so I'll finish explaining why this is interesting tomorrow.