Suppose there is a correspondence between letters and numbers where each letter is repre- sented by the number shown below. Spaces are ignored. AB C DEF J K L M 1 2 3 4 5 6 9 10 11 12 13 V W X Y Z NO P Q R S 14 15 16 17 18 19 20 21 22 23 24 25 26 GH I C1E9 HUN T 12 8 To write your message in numbers, you divide the message in pairs of letters and associate them to the following numbers. For example if you want to encode the word "elephant" you start with the pre-encoded message 5 E 5 14 (3-6) (-6) (2)-(3) (G)-(C)- (2). 12 P 16 20 which results in 0000 5 16 20 To encode a message using a matrix A, you need to multiply A on the left by each two letter 2 message. If A = -(43) you encode the first two letters EL with SO 5 (B)(6)-(C) You repeat the same procedure for the entire pre-encoded message and create the encoded message. To decode the message, you multiply A- to the left with each pair. For example to decode 29 (9). 7 , you find the inverse of A which is A *'-(17) 12 which corresponds to the letters EL and then you apply the same procedure to all the encoded message.. 29 (a) Use matrix B= (31) 2 (b) Decode the following message that was encoded using B to encode the message "COME ON". (8) ( ) ( ) ( ) -37 -39 -32 (c) Is it possible to use the matrix C= Explain why. 2 2 to encrypt and decrypt messages?