In addition to eigenvectors and eigenvalues, other unique properties of matrices and vectors can be visualised geometrically. Commutation is a shared property of two matrices defined by: $$ \bf{\color{#0091D4}A\color{#EC7300}B = \color{#EC7300}B\color{#0091D4}A} $$ Geometrically speaking, this means that applying the spacial transformations A then B is identical to applying the transformation B then A. Select your own custom two transforms to the initial black vector and press play! You will see that the final white and black vectors represent:

△: A B
▲: B A

If these white and black vectors end up at the same point then the two transformations commute! In the case of the two transformations you have selected, they do commute.


Transform A:
about

Transform B:
about