Supppose $A$ is an invertible $n\times n$ matrix and $\vec{v}$ is an eigenvector of $A$ with associated eigenvalue $3$. Convince yourself that $\vec{v}$ is an eigenvector of the following matrices, and find the associated eigenvalues.

1. The matrix $A^{3}$ has an eigenvalue .
   
   
2. The matrix $A^{-1}$ has an eigenvalue .
   
   
3. The matrix $A + 8 I_n$ has an eigenvalue .
   
   
4. The matrix $-6 A$ has an eigenvalue .