Answer
please see step by step.
Work Step by Step
A .B C D E F G H I....
1.. 2 .3 4 5 6 7 8 9...
H,E,L,P $\leftrightarrow$ 8,5,12,16
Encoding with A:
$\left[\begin{array}{ll}
4 & -1\\
-3 & 1
\end{array}\right]\left[\begin{array}{l}
8\\
5
\end{array}\right]=\left[\begin{array}{l}
32-15\\
-24+5
\end{array}\right]=\left[\begin{array}{l}
27\\
-19
\end{array}\right]$
$\left[\begin{array}{ll}
4 & -1\\
-3 & 1
\end{array}\right]\left[\begin{array}{l}
12\\
16
\end{array}\right]=\left[\begin{array}{l}
48-16\\
-36+16
\end{array}\right]=\left[\begin{array}{l}
32\\
-20
\end{array}\right]$
HELP is encoded into $27,-19,32,20.$
Decoding with $A^{-1}$
$\left[\begin{array}{ll}
1 & 1\\
3 & 4
\end{array}\right]\left[\begin{array}{l}
27\\
-19
\end{array}\right]=\left[\begin{array}{l}
27-19\\
81-76
\end{array}\right]=\left[\begin{array}{l}
8\\
5
\end{array}\right] \quad...\left(\begin{array}{l}
H\\
E
\end{array}\right)$
$\left[\begin{array}{ll}
1 & 1\\
3 & 4
\end{array}\right]\left[\begin{array}{l}
32\\
-20
\end{array}\right]=\left[\begin{array}{l}
32-20\\
96-80
\end{array}\right]=\left[\begin{array}{l}
12\\
16
\end{array}\right] \quad...\left(\begin{array}{l}
L\\
P
\end{array}\right)$
