Given the matrix [mathbf{C}(z)=left[begin{array}{ccc}R_{0}(z) & R_{1}(z) & R_{2}(z) z^{-1} R_{2}(z) & R_{0}(z) & R_{1}(z) z^{-1} R_{1}(z) & z^{-1} R_{2}(z) & R_{0}(z)end{array} ight]] verify if (mathbf{C}^{2}(z))

Given the matrix

\[\mathbf{C}(z)=\left[\begin{array}{ccc}R_{0}(z) & R_{1}(z) & R_{2}(z) \\z^{-1} R_{2}(z) & R_{0}(z) & R_{1}(z) \\z^{-1} R_{1}(z) & z^{-1} R_{2}(z) & R_{0}(z)\end{array}\right]\]

verify if \(\mathbf{C}^{2}(z)\) is pseudo-circulant.