Discrete Math Help!

Consider the following matrices. A 12 2 1 11 1 2 3 1 11 2 3 1112 and C 11 11 2 3 , B -[ ], - | For this problem, you must calculate the product P = ABC. But wait! Don't start yet! Matrix multiplication is associative, which means we can calculate the product P by first computing the matrix (AB), then multiplying this by C to obtain P = (AB)C. Or we could first compute the matrix (BC), then multiply it by A to obtain P = A(BC). Furthermore, to multiply an m x n matrix by an n x k matrix requires m x n x k multiplications. Note: we are only counting multiplications here. (a) Suppose A is m x n, B is n x k and C is kx p. How many multiplications are needed to calculate P in the order (AB)C ? Do not just write down an expression; show your work/justification! (b) For the same matrix dimensions specified in (a), how many multiplications are needed to calculate P in the order A(BC) ? Again, do not just write down an expression. (c) Based on the specific dimensions of A, B, and C in the problem description, which multiplication order would be the most efficient? (d) Calculate P = ABC using whichever order you specified in part (c )