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 $A$?
- $\begin{bmatrix}
0\\
0\\
-1
\end{bmatrix}$
- $\begin{bmatrix}
-1\\
0\\
0
\end{bmatrix}$
- $\begin{bmatrix}
1\\
0\\
-1
\end{bmatrix}$
- $\begin{bmatrix}
1\\
-1\\
1
\end{bmatrix}$