Oh hey, that's actually really cool. I never knew how matrix multiplication worked. Honestly, there's a lot of maths I don't necessarily understand as well as I should, but this gives me hope that I will one day be able to get that understanding.
The wiki article on it has a number of good illustrations to show it as well. Moreover, I find the cognitive leap from matrix multiplication to simultaneous equations very powerful and enlightening, particularly when you then understand the wide application of simultaneous equations.
Also, I encourage you to play with trying to shrink/expand the rows/columns of each matrix and seeing how it enforces certain rules on the other matrix. Once you mentally picture what'd happen if it didn't viz the animation that the site plays when you hit 'go', you begin to understand it better.
