It (presumably) started with the assumption that you already know what a determinant is and does, then it described how to calculate it, commutativity propertie

It (presumably) started with the assumption that you already know what a determinant is and does, then it described how to calculate it, commutativity properties etc... but never the geometrical interpretation, which would have helped greatly. Imagine somebody describes a triangle to you by telling you all the mathematical properties of triangles (angle sums, pythagorean theorem, all the trig functions), but never saying it's a polygon with three edges.