im tryna using matrices for encryption of sorts. I have my message as $Matrix M = {{8,5,12,12,4}, {23,15,18,12,4}}$.
My encoder as $Matrix E = {{3,4},{-1,2}}$ I multiply M by E to give me matrix C $EM = C$ where $Matrix C = {{116, 75, 108, 84, 61},{38, 25, 24, 12, -7}}$.
When I try to decrypt $Matrix C$ with the inverse of $Matrix E$; $E'EM = E'C ; M = E'C$, I have my $Matrix E' = {{2/10, -4/10}, {1/10, 3/10}}$ so I do the following $E'C = {{2/10, -4/10}, {1/10, 3/10}} * {{116, 75, 108, 84, 61},{38, 25, 24, 12, -7}} = {{-18/5, -5/2, 6/5, 18/5, 89/10}, {23, 15, 18, 12, 4}}$