Consider
$T_{2}: \left[ \begin{array}{cc} a & b \\ c & d \\ \end{array} \right] \rightarrow \left[ \begin{array}{cc} d & c \\ b & a \\ \end{array} \right] $
$T_{3}: \left[ \begin{array}{ccc} a & b &c \\ d & e & f \\ g & h & i \end{array} \right] \rightarrow \left[ \begin{array}{cc} i & h & g \\ f & e & d\\ c & b & a \\ \end{array} \right] $
- What is the appropriate name for this sort of transformation? (googling for combinations of 'matrix' and 'rotation" hasn't been fruitful for obvious reasons).
- I know that $T_{n}$ is an involution -- $T_{n}^{2}=I_{n}$ -- but I don't know what effect it has in general, that is, what it does to $GL_{n}(\mathbb{R})$ or anything else representable by $n\times n$ matrices. (the motivation for this question is the effect of $T_{2}$ on the modular group $SL(2,\mathbb{Z})$)