For the group \(\{\mathbf{E}, \mathbf{T}\}\), the regular representation for \(\mathbf{T}\) is \(\left(\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}ight)\). A similarity transformation with a matrix \(S\) reduces it to the block diagonal form \(\left(\begin{array}{ll}1 & 0 \\ 0 & a\end{array}ight)\). Show that \(a= \pm 1\) and choose the correct value by calculating the matrix \(\mathbf{S}\). Show that your matrix is unitary \(\mathbf{S S}^{\dagger}=\mathbf{E}\).