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