Answer both parts (a) and (b). Please explain your reasoning and show your work:

Question 6 (9 marks) Look at the following picture in the 2D plane, which shows a red square A(2, 1), B(2, 2), C(1, 2), and D(1, 1). Let's scale it in the direction as shown in the figure. B D A The x direction should be scaled 3 times while the y direction should be scaled 2 times. During the scaling, keep point A fixed. (So after the scaling, the square changes to something like the one shown in blue. The blue rectangle in the figure is just for illustration purpose.) (a) (5 marks) Derive the matrices that do the above operation and show them in the correct order, i.e., show a matrix first if the transformation corresponding to the matrix is done first (b) (4 marks) Calculate the new coordinates of points C and D using the matrices in (a)