Matrices Cryptology

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Frances and Ivy are good friends. They often leave messages for each other by e-mail. To prevent their brothers from intercepting and understanding their mail, the girls decide to encode their messages.

They propose a matrix code based on the date a message is sent. They agree to use a 3×3 encoding matrix with the ‘date sent’ filling the first 8 entries. The ninth element is determined by the first letter of the sender’s name. Also based on date sent, they agree to pre-multiply on an even day of a month but post-multiply on an odd day. So, for a message sent on 4th March, 2000 by Frances, the encoding matrix would have the elements 0 4 0 3 2 0 0 0 6 and this 3×3 encoding matrix would form the left-hand factor of any product.

Frances receives an e-mail from her friend dated 13/05/2000. It reads: 
“60 76 81 34 63 135 29 22 81 24 59 207 79 55 126 95 51”.

Make sense of (decode) this message for Frances.

Some earlier questions used modulo 26


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