Please Help With Python Coding

Finding the Eigenvalues and Eigenvectors of a Matrix

Let $A$ be the matrix given below.

$A=\left[\begin{array}{ccc}4& 0& 1\\ -1& -6& -2\\ 5& 0& 0\end{array}\right]$

$($a$)$ Is the vector $\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$ an eigenvector of $A?$ Verify your answer with a calculation in Python.

$($b$)$ Is the vector $\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right]$ an eigenvector of A$?$ Again, verify your answer with a calculation in Python.

$($c$)$ Use Python to find all of the eigenvalues and eigenvectors of $A.$