Problem $1$: Consider the table below which provides a numerical coding scheme:

$\backslash$table$[[$A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I,J$,$K$,$L$,$M$,$N O$,$P$,$Q$,$R$,$S$,$T$,$U$,$V$,$W$,$X$,$Y$,$Z$,],[8,7,5,13,9,16,18,22,4,23,11,3,21,1,6,15,12,19,2,14,17,20,25,24,10,26]]$

Create a 'secret code' which is nine letters long and encode it using a $33$ matrix. Let us refer to this matrix as $M_{{?}_{?}}$

Create an encoding $33$ matrix $C_{{?}_{?}}.$

Compute $C_{{?}_{?}}*M_{{?}_{?}}.$ How does this new matrix read when you tranlate it using the table above?

Compute $M_{{?}_{?}}^{-1}$

What does the alphabetical code read if you use the encoding matrix $B_{{?}_{?}}$ which is given below?

$B_{{?}_{?}}=\left[\begin{array}{ccc}2& 1& 3\\ 0& 2& 4\\ 1& 1& 2\end{array}\right]$

Given the matrix $B_{{?}_{?}}*M_{{?}_{?}},$ can you recover the original secret code? If not, why not?

Is $B_{{?}_{?}}$ a symmetric matrix? If not, can you symmetrize it$?$

Find the transpose of $B_{{?}_{?}}$