Answer
$$0$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
3 & 3 & { - 1} \cr
2 & 6 & 0 \cr
{ - 6} & { - 6} & 2 \cr
} } \right| \cr
& {\rm{Calculating\, the\, determinant\, by \,expanding\, the\, third\, column}} \cr
& \left| {\matrix{
3 & 3 & { - 1} \cr
2 & 6 & 0 \cr
{ - 6} & { - 6} & 2 \cr
} } \right| = - 1\left| {\matrix{
2 & 6 \cr
{ - 6} & { - 6} \cr
} } \right| - 0\left| {\matrix{
3 & 3 \cr
{ - 6} & { - 6} \cr
} } \right| + 2\left| {\matrix{
3 & 3 \cr
2 & 6 \cr
} } \right| \cr
& {\rm{Solving}} \cr
& \left| {\matrix{
3 & 3 & { - 1} \cr
2 & 6 & 0 \cr
{ - 6} & { - 6} & 2 \cr
} } \right| = - 1\left( { - 12 + 36} \right) - 0 + 2\left( {18 - 6} \right) \cr
& {\rm{Simplifying}} \cr
& \left| {\matrix{
3 & 3 & { - 1} \cr
2 & 6 & 0 \cr
{ - 6} & { - 6} & 2 \cr
} } \right| = 0 \cr} $$
