Use homogeneous coordinates for the following problem.

Let A and B denote order-4 matrices, and let p be a point in homogeneous coordinates (4 by 1 matrix with last component equal to 1). Specify the number of multiplies required to compute (a) (A B)p and (b) A(B p). Note that no multiplies are required to compute the last row of (A B) or the last component of (B p). Explain why it is usually advantageous to combine transformations before applying them (despite the fact that case (a) requires more multiplications).