The matrix $A=\begin{bmatrix} \frac{3}{2} &0 & \frac{1}{2}\\ 0& -1 &0 \\ \frac{1}{2} & 0 & \frac{3}{2} \end{bmatrix}$ has three distinct eigenvalues and one of its eigenvectors is $\begin{bmatrix} 1\\ 0\\ 1 \end{bmatrix}$. Which one of the following can be another eigenvector of $A$?

1. $\begin{bmatrix} 0\\ 0\\ -1 \end{bmatrix}$
2. $\begin{bmatrix} -1\\ 0\\ 0 \end{bmatrix}$
3. $\begin{bmatrix} 1\\ 0\\ -1 \end{bmatrix}$
4. $\begin{bmatrix} 1\\ -1\\ 1 \end{bmatrix}$