The inverse of the matrix \[\left[ {\begin{array}{*{20}{c}} 2&3&4 \\ 4&3&1 \\ 1&2&4 \end{array}} \right]\]  is

A. \[\left[ {\begin{array}{*{20}{c}} {10}&{ - 4}&{ - 9} \\ { - 15}&4&{14} \\ 5&{ - 1}&{ - 6} \end{array}} \right]\]

B. \[\left[ {\begin{array}{*{20}{c}} { - 10}&4&9 \\ {15}&{ - 4}&{ - 14} \\ { - 5}&1&6 \end{array}} \right]\]

C. \[\left[ {\begin{array}{*{20}{c}} 2&{ - \frac{4}{5}}&{ - \frac{9}{5}} \\ { - 3}&{\frac{4}{5}}&{\frac{{14}}{5}} \\ 1&{ - \frac{1}{5}}&{ - \frac{6}{5}} \end{array}} \right]\]

D. \[\left[ {\begin{array}{*{20}{c}} { - 2}&{\frac{4}{5}}&{\frac{9}{5}} \\ 3&{ - \frac{4}{5}}&{ - \frac{{14}}{5}} \\ { - 1}&{\frac{1}{5}}&{\frac{6}{5}} \end{array}} \right]\]

Answer: Option D