The determinant is the signed area of a parallelogram | Abstract Algebra 7

"Proof-by-picture" that the determinant of a 2x2 matrix is the signed area of the parallelogram spanned by its columns.

The goal of this mini-series is to try to answer: "what does the determinant of a matrix have to do with it being invertible". More generally, my aim is to untie the knots most people have in their head about basic things in linear algebra.