Category:Group of Reflection Matrices Order 4

Group of Reflection Matrices Order $4$

Consider the algebraic structure $S$ of reflection matrices:

$R_4 = \set {\begin {bmatrix} 1 & 0 \\ 0 & 1 \end {bmatrix}, \begin {bmatrix} 1 & 0 \\ 0 & -1 \end {bmatrix}, \begin {bmatrix} -1 & 0 \\ 0 & 1 \end {bmatrix}, \begin {bmatrix} -1 & 0 \\ 0 & -1 \end {bmatrix} }$

under the operation of (conventional) matrix multiplication.

$R_4$ is the group of reflection matrices of order $4$.