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## Orthogonal Transformations _ Benson and Grove on Finite Reflection Groups

 Quote by Math Amateur Thanks Fredrik Definitely dealihng with case $\mathbb{R^2}$ Will just reflect on what you wrote! Still puzzling a bit about showing that $T e_2 = \pm ( - \nu , \mu)$ Peter
You know that Te2 is the second column of T, that ##(\mu,\nu)## is the first column, and that the columns are orthonormal. So you only have to prove that if ##(\alpha,\beta)\cdot (\mu,\nu)=0## and ##|(\alpha,\beta)|=1##, then ##(\alpha,\beta)=\pm(-\nu,\mu)##.