This is cool, but I have a few criticisms:

- Flipping something over like that looks cool, but confuses the brain. At least it confused mine.

- Inconsistently calculating 1 or 2 elements at a time is confusing. Having 2 results calculated at a time simply put requires the recipient to untangle what is going on. This only gets worse when the recipient tries to do it themselves for examples with more columns in the right matrix.

Disclaimer: I am biased as I already know how to do matrix operations, and I visualize it differently. When multiplying by hand I translate the right matrix up, like in the animation, but do not flip it over. Then I calculate each element one at a time by taking the sum of products of the row and column that intersects over that element. Like so: http://i.imgur.com/D572zOI.png

As you can see I'm not much of a graphics artist.

Edit: actually, I think this would be really good if you "filter down" one column at a time, instead of moving the whole matrix down, so that it only calculates one element at a time, one column at a time. Means the animation will contain more steps, but I think that is actually to its benefit. Does this make sense?