1.4.22 Matrix transformations

Condition: Given a matrix \( A=\left(\begin{array}{ccc}1 & 2 & -2 \\ -1 & 4 & -2 \\ 1 & 2 & -2\end{array}\right) \) : a) find the eigenvalues ​​of the matrix \( A \); b) find the eigenvectors of the matrix \(A\); c) find out whether the matrix \(A\) is similar to a diagonal matrix and, if it is similar, then find the matrices \(C\) and \(D(D-\) diagonal matrix) such that \(A=C D C^{-1}\).