Linear Algebra - Eigenvalues and Eigenvectors

Two $n \times n$ matrices $A$ and $B$ have a common eigenvalue 2, and the same corresponding nonzero eigenvector. Which of the following options is/are correct? (Note: $I$ is the $n \times n$ identity matrix.)

The matrix A = $\begin{bmatrix} 3/2 & 0 & 1/2 \ 0 & -1 & 0 \ 1/2 & 0 & 3/2 \end{bmatrix}$ has three distinct eigenvalues and one of its eigenvectors is $\begin{bmatrix} 1 \ 0 \ 1 \end{bmatrix}$. Which one of the followin...