The maximum value of "a" such that the matrix \[\left( {\begin{array}{*{20}{c}} { - 3}&0&{ - 2} \\ 1&{ - 1}&0 \\ 0&{\text{a}}&{ - 2} \end{array}} \right)\]   has three linearly independent real eigen vectors is

A. \[\frac{2}{{3\sqrt 3 }}\]

B. \[\frac{1}{{3\sqrt 3 }}\]

C. \[\frac{{1 + 2\sqrt 3 }}{{3\sqrt 3 }}\]

D. \[\frac{{1 + \sqrt 3 }}{{3\sqrt 3 }}\]

Answer: Option B