Activity $2($Design your own substitution cipher$)$

$($a$)$ Use the criteria indicated to create a pair of $33$ matrices $(D$&$D^{-1}),$ where the entries

of the matrix $D$ are all integers.

$(20$ marks $)$

$($i$)d_{2,1}=5$

$($ii$)d_{3,2}=-2$

$($b$)$ Create your own substitution cipher. Then use it and the matrix $D$ you created in $($a$)$ to

encrypt the title of your favourite movie.

$(20$ marks $)$

$($c$)$ Use the matrix $D^{-1}$ and the appropriate substitution cipher to decrypt the message from

$($b$).$

$(20$ marks $)$Activity $1($Unlock a coded message$)$

Doctor Strange is in deep trouble. He is being pursed by Thanos and is presently hiding in a secret

location to escape from being captured by him. He needs to send messages to two of his comrades,

Thor and Captain America, to tell them about his situation and whereabouts. As such, he composes

his first message by replacing each letter in the message by a number according to the code in

Table $1$ below.

Table $1$: Coding system

As Doctor Strange is afraid that his message will be intercepted and cracked by Thanos, therefore,

he decides to send the message in code together with a super hi$-$tech LOCK to Thor and Captain

America to unlock the coded message.

LOCK $=\left[\begin{array}{ccc}1& 0& 1\\ -1& 1& 0\\ 0& 1& 2\end{array}\right]$

With the use of Table $1$ and LOCK, what is the message that Doctor Strange is trying to send to Thor

and Captain America? Please show your working clearly on how you unlock the code message.