9 The square matrix \(\mathbf { A }\) has an eigenvalue \(\lambda\) with corresponding eigenvector \(\mathbf { e }\). The non-singular matrix \(\mathbf { M }\) is of the same order as \(\mathbf { A }\). Show that \(\mathbf { M e }\) is an eigenvector of the matrix \(\mathbf { B }\), where \(\mathbf { B } = \mathbf { M } \mathbf { A } \mathbf { M } ^ { - 1 }\), and that \(\lambda\) is the corresponding eigenvalue. Let $$\mathbf { A } = \left( \begin{array} { r r r } - 1 & 2 & 1
0 & 1 & 4
0 & 0 & 2 \end{array} \right)$$ Write down the eigenvalues of \(\mathbf { A }\) and obtain corresponding eigenvectors. Given that $$\mathbf { M } = \left( \begin{array} { l l l } 1 & 0 & 1
0 & 1 & 0
0 & 0 & 1 \end{array} \right)$$ find the eigenvalues and corresponding eigenvectors of \(\mathbf { B }\).