matrix multiplication square X column (post multiply)
Another common multiplication is between a square matrix and a column matrix. This too is used for transforming a point. The only difference is that the point is now represented by a column matrix. The rules for matrix multiplication require that we put the column matrix after the square matrix instead of in front of it as in the previous row examples. The example below shows the order they should be in for a three by three square multiplied by a 3 element column matrix. In this case, the elements of the column are multiplied by the rows of the square matrix which results in a three element column for the answer. This is a post multiply. In the case of a four element column and its 4X4 square, the procedure is the same except that the answer is a four element column. As you become familiar with the shapes of matrices, you will see that the row multiply and the column multiply produce the same results but the rows and columns are swapped. We'll discuss that just ahead.
