A matrix moves the plane

Change the four numbers of a 2×2 matrix and watch what it does to the grid, the unit square, and its eigenvectors.

The matrix A = [[a, b], [c, d]]

a (top left)b (top right) c (bottom left)d (bottom right)

Try thisFind a matrix with det = 0 by hand (the square collapses to a line). Then press "rotate 90°": why are there no yellow eigenvector lines?