\begin{definition}[Definition:Group of Rotation Matrices Order 4]
Consider the algebraic structure $S$ of rotation matrices:
:$R_4 = \set {\begin {bmatrix} 1 & 0 \\ 0 & 1 \end {bmatrix}, \begin {bmatrix} 0 & 1 \\ -1 & 0 \end {bmatrix}, \begin {bmatrix} -1 & 0 \\ 0 & -1 \end {bmatrix}, \begin {bmatrix} 0 & -1 \\ 1 & 0 \end {bmatrix} }$
under the operation of (conventional) matrix multiplication.
$R_4$ is the '''group of rotation matrices of order $4$'''.
\end{definition}