I don't know why but it seems to make more sense to me if I think of the multiplication in terms of rotating or transposing and moving the vector or matrix so t

I don't know why but it seems to make more sense to me if I think of the multiplication in terms of rotating or transposing and moving the vector or matrix so that the columns or rows line up with the ones they are to be multiplied with, the coloured guides are entirely useless to me.