For the following matrix $A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 2& 1\\ 0& 0& 3\end{array}\right],$

$1-$find the eigenvalues and eigenvectors of $A.$

$2-$

Is the matrix A diagonalizable? Justify your answer

$3-$

Find the eigenvalues of $A^2?$

$4-$

Find the eigenvalues of $A^{-1}?$

$5-$

Find the eigenvalues of $A^T?$

$6-$

Find the eigenvalues of $2A.$