mud D lb} SupposeA = and B =[_01 0 J. 1 C2- 1 2 ii} Compute the product AB. iii) Compute the product BA. {iii} How do your answers in parts (i} and {ii} compare? Will this be true in general for any two matrices when you multiply them (assuming their dimensions line up so they can be multiplied]? If so, defend your reasoning. If not, then supply an example of two matrices, C and D, such that CD sf: DC. Part llApplication For this problem, you will apply your knowledge of matrix multiplication and inverses to an application. A cryptogram is a message written according to a secret code. For this cryptogram, we assign numbers to letters and characters as follows: (i.. 0: 13:3 27: 1:11 13:.1 13:3 23 2:3 11:3 23=T 29: 3=C 12=L 21:1 33:1 4:1) 13:31 22:1; 31: 52E 14:5: 23:11' :2: 3:3 13:0 24=x 33:" T=G 13:19 23:3 :u=' 3:11 lT=Q 23:2 :3:/ Suppose that you received the following numerical information for a top-secret transmission: (a) [67 113 47] (b} [3 13 14] (cl [31 150 93] (d} [111 213 134] (e) [3 13 14] if) [23 26 13] (g) [23 41 23] in} [133 257 153] Suppose that you received the following numerical information for a topsecret transmission: (a) [6? 113 47] lb}- [9 13 14] (c) [81 150 490] (a:- [111 210 134] (e) [9 13 14] [n [20 2e 13] lg} [23 41 20] (h}- [139 25:r 150] 1 1 2 Suppose you were sent the coding matrix: A = 2 4 3'. The coding matrix can be thought of as 3 6 5 the \"key\" to unlock the message. Use the coding matrix along with the numerical information {ag] and follow the process in Section 8.5 of the textbook to decode the message. Write your answer in the space provided below. Be sure to include all your work on a separate sheet of pa per. Decoded Message