For the group of an equilateral triangle, let operation A be a "flip" - a rotation by \(180^{\circ}\) about the \(y\)-axis. Show that \(\phi_{1}=x^{2}+y^{2}\) and \(\phi_{2}=z\) are basis functions for \(\mathbf{A}\) by finding the corresponding matrix representation for \(\mathbf{A}\).

Transcribed Image Text:

Z y