Problem $2\mathrm{.}7.(8+2$ points$)$ The matrices

$A=\left[\begin{array}{ccc}3& 1& 2\\ 2& 1& -1\\ 3& 1& 3\end{array}\right],$ and $B=\left[\begin{array}{ccc}4& -1& -3\\ -9& 3& 7\\ -1& 0& 1\end{array}\right]$

are mutual inverses.

$($a$)$ Modify the encryption python code from class so that it uses $A$ to

encrypt a message and then encrypt the message

THE PLOT THICKENS

using your new program $($replacing spaces by #$).$ Submit the encrypted

message and your program code.

$($b$)$ How would you produce your own $33$ matrix A with all entries non$-$

zero so that A has an inverse?