The line joining (1,0) and (0,2) has a slope (2-0)/(0-1)=-2. The line joining (0,2) and (1,0) has a slope (0-2)/(1-0)=-2. So these points are colinear because (0,2) is a common point and the lines have the same slope.
The determinant is:
| 1 0 1 |
| 0 2 1 | = 1(2-0)-0+1(0-2)=2-2=0 which confirms collinearity.
| 1 0 1 |