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