Question

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Answer 1

these are reflections across the line y = -x

Answer 2

yeee gads, a Rotation Matrix ... if you like Matrix Algebra .... reflecting stuff about the line y = -x:

\(R (\mathbf x ) = \left[\begin{matrix}0 & -1 \\ -1 & 0\end{matrix}\right]\)

Answer 3

Methuselah(!!), a Reflection Matrix ...:
\[R(\mathbf x) = \left[\begin{matrix}0 & -1 \\ -1 & 0\end{matrix}\right] \qquad x \in \mathcal R^2\]