Following the video from MIT's OCW, the Prof. brings up many different methods, like $row * matrix$, $column * matrix$, etc. Yet don't these all come down to dot product. For example $row * matrix$ would be done using dot product, right? Is the Prof just showing all of these things to show the big picture, or what?
A little bonus: The Prof says that with the multiplication of the matrices A and B (AB) equaling to C, that the rows of C are a combination of the rows of A. Here, the columns of B must be multiplied by the matrix A (column * matrix method) to get one column of C. So, to do this you would end up doing the columns of B times all the rows of A (using dot product, right, question above), yet he says that the columns of C are a combination of the columns of A, is this just because when doing all of the rows, the columns will technically be included?
Thanks for all the help!
Whatever the method, the final result is uniquely defined. So you can say that it amounts to dot products.
For practical reasons, the order of the operations can make a difference in convenience or speed when you multiply on paper or with a computer. When there is numerical truncation, even the values can differ.