91Ó°ÊÓ

If \(X\) is a \(G\) -set, then each of its orbits is a transitive \(G\) -set.

If \(\Delta\) is an equilateral triangle in \(\mathbb{R}^{2}\) with its center of gravity at the origin, show that \(\mathscr{f}(\Delta)\) is generated by $$ A=\left[\begin{array}{cc} -\frac{1}{2} & \sqrt{3} / 2 \\ \sqrt{3} / 2 & -\frac{1}{2} \end{array}\right] \text { and } B=\left[\begin{array}{rr} 1 & 0 \\ 0 & -1 \end{array}\right] \text { . } $$