Neat visualization. I feel it's important and eye-opening to note that there's not just one way to multiply matrices, there're five (according to Strang):

5 ways to multiply A B = C

1) Each element of C is a dot-product of corresponding rows of A with columns of B

2) Each column of C is a combination of the columns A. Each column of B has the coefficients.

3) Each row of C is a combination of the rows of B. Each row of A has the coefficients.

4) Accumulate outer-product. Accumulate sums of of outer-products of each col of A with each row of B.

5) Block multiplication

They all produce the same answer, but different ones provide different insight for particular situations.

See Video Lecture #3 of Strang's Linear Algebra course for more info: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...