A \(3 \times 3\) matrix \(\mathbf { A }\) has eigenvalues \(- 1,1,2\), with corresponding eigenvectors
$$\left( \begin{array} { r }
0
1
- 1
\end{array} \right) , \quad \left( \begin{array} { r }
- 1
0
1
\end{array} \right) , \quad \left( \begin{array} { l }
1
1
0
\end{array} \right) ,$$
respectively. Find
- the matrix \(\mathbf { A }\),
- \(\mathbf { A } ^ { 2 n }\), where \(n\) is a positive integer.