Chapter 8 - Section 8.4 - Multiplicative Inverses of Matrices and Matrix Equations - Exercise Set - Page 933: 54

The matrix is $\left[ \begin{matrix} -1 & 25 & -7 \\ 59 & 121 & 39 \\ -20 & -48 & -17 \\ \end{matrix} \right]$ and the decoded message is $\left[ \begin{matrix} 19 & 25 & 5 \\ 20 & 0 & 12 \\ 1 & 23 & 12 \\ \end{matrix} \right]$.

Consider the given expression, $ STAY\_WELL $ Therefore, $\begin{align} & S=19 \\ & T=20 \\ & A=1 \\ & Y=25 \\ \end{align}$ Also, $\begin{align} & W=23 \\ & E=5 \\ & L=12 \\ & L=12 \\ \end{align}$ Using the cryptogram method we get, $\begin{align} & A=\left[ \begin{matrix} 1 & -1 & 0 \\ 3 & 0 & 2 \\ -1 & 0 & -1 \\ \end{matrix} \right]\left[ \begin{matrix} 19 & 25 & 5 \\ 20 & 0 & 12 \\ 1 & 23 & 12 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 19-20+0 & 25+0+0 & 5-12+0 \\ 57+0+2 & 75+0+46 & 15+0+24 \\ -19+0-1 & -25+0-23 & -5+0-12 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} -1 & 25 & -7 \\ 59 & 121 & 39 \\ -20 & -48 & -17 \\ \end{matrix} \right] \end{align}$ Therefore, expression of the matrix is $\left[ \begin{matrix} -1 & 25 & -7 \\ 59 & 121 & 39 \\ -20 & -48 & -17 \\ \end{matrix} \right]$.