Whenever I teach computer graphics, one of the most important topics is learning how to work with 4×4 matrices. 4×4 matrices are the workhorse, not just of computer graphics, but of many scientific fields, including robotics, aerospace, medical imaging and quantum mechanics, to name just a few.
One of the odd properties of matrices is that multiplication order matters. When you multiply two number, say 11×13, you get the same result as when you multiply 13×11. But if you multiply two matrices A and B, the product AxB is usually different from the product BxA.
I needed to find a way to make this intuitive for my students, so I wrote a little visualization to help them think it through. You can try it for yourself HERE.
I’m teaching the same class and going through the exact same thought process. My similar response was to build Transformula (https://transformula.twodee.org/) as a sandbox for playing around with transformations. They can be arbitrarily composed, reordered, toggled, parametrically tweaked, and annotated by their basis. We spent all of Thursday’s lab using it to get a feel for matrix transformations.