The matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} {\frac{3}{2}}&0&{\frac{1}{2}} \\ 0&{ - 1}&0 \\ {\frac{1}{2}}&0&{\frac{3}{2}} \end{array}} \right]\]   has three distinct eigen values and one of its eigen vectors is \[\left[ {\begin{array}{*{20}{c}} 1 \\ 0 \\ 1 \end{array}} \right].\]
Which one of the following can be another eigen vector of A?

A. \[\left[ {\begin{array}{*{20}{c}} 0 \\ 0 \\ { - 1} \end{array}} \right]\]

B. \[\left[ {\begin{array}{*{20}{c}} { - 1} \\ 0 \\ 0 \end{array}} \right]\]

C. \[\left[ {\begin{array}{*{20}{c}} 1 \\ 0 \\ { - 1} \end{array}} \right]\]

D. \[\left[ {\begin{array}{*{20}{c}} 1 \\ { - 1} \\ 1 \end{array}} \right]\]

Answer: Option C