Determinant
Determinant
Determinant means the area of the unit area after the transformation.
You can prove the formula on geometry
What does a negtive number of a determinant mean.
Calculating 3-D determinant means the volume of a parallelepiped.
The direction of a 3-D transformation satisfies right hand rule, if not the result of the determinant should be negtive.
Reference
https://www.3blue1brown.com/topics/linear-algebra