Typically, this visualization isn't taught, in my experience. What's taught is the formula for computing each cell of the result matrix (cell i,j being the dot

Typically, this visualization isn't taught, in my experience. What's taught is the formula for computing each cell of the result matrix (cell i,j being the dot product of row i of the first matrix with column j of the second). While this is, of course correct, and also the most efficient way to compute the multiplication manually, it's not always clear why the formula is correct. Hopefully the visualization on the linked page makes this formula's origin clear.