Which one of the following is an eigen vector of the matrix \[\left[ {\begin{array}{*{20}{c}} 5&0&0&0 \\ 0&5&5&0 \\ 0&0&2&1 \\ 0&0&3&1 \end{array}} \right]?\]

A. \[\left[ {\begin{array}{*{20}{c}} 1 \\ { - 2} \\ 0 \\ 0 \end{array}} \right]\]

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

C. \[\left[ {\begin{array}{*{20}{c}} 1 \\ 0 \\ 0 \\ { - 2} \end{array}} \right]\]

D. \[\left[ {\begin{array}{*{20}{c}} 1 \\ { - 1} \\ 2 \\ 1 \end{array}} \right]\]

Answer: Option A