A 2-dimensional representation of a group member \(\mathbf{T}\) is generated by the \(\alpha\) set of basis functions to give \(D^{(\alpha)}(\mathbf{T})=\left(\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}ight)\) and by the \(\beta\) set of basis functions to give \(D^{(\beta)}(\mathbf{T})=\left(\begin{array}{cc}-1 & 0 \\ 0 & 1\end{array}ight)\). Show that these representations are equiv alent, related by a similarity transformation with \(\mathbf{S}\). Show that your \(\mathbf{S}\) is unitary \(\mathbf{S S}^{\dagger}=\mathbf{E}\).