I wouldn't teach it that way, you're teaching 2 non-standard matrix operations, and matrix multiplication is simple enough on the face of it that there's no need to build up to it with additional layers.
You also lose an intuitive property of matrix multiplication, that you can figure out where the resulting element value goes in terms of which row and which column you're iterating over. If you're iterating over the second row of the left-hand side matrix, and the third column of the right-hand-side matrix, that implies the resulting value must go in the second row, third column, of the result matrix.
Matrix multiplication can easily be visualised and taught in terms of dot products, without using additional transformations. An example: https://www.mathsisfun.com/algebra/matrix-multiplying.html
