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