I have learned a shortcut for finding eigen values and characteristic equation. It is as follows.
$\lambda ^{_{3}}- \alpha \lambda ^{2}+ \beta \lambda - \gamma =0$
where $ \alpha =$ trace of 3*3 matrix
$ \beta =$ sum of cofactor of diagonal elements
$ \gamma =$ det of 3*3 matrix
when I follow this logic in the below problem I'm stuck, Could any one help me find why I'm stuck . I was getting answer using this trick for almost all problems