Answer
$X=\begin{bmatrix}
-1& -2\\
4 &1
\end{bmatrix}$
Work Step by Step
Begin by finding the inverse of A
$A^{-1}=\frac{1}{-24-0}\begin{bmatrix}
6 & -1\\
0 & -4
\end{bmatrix}=\begin{bmatrix}
\frac{-1}{4}& \frac{-1}{8}\\
0 &\frac{1}{6}
\end{bmatrix}$
To solve the equation for X:
$A^{-1}AX=A^{-1}B$
$\begin{bmatrix}
\frac{-1}{4}& \frac{-1}{8}\\
0 &\frac{1}{6}
\end{bmatrix}\begin{bmatrix}
-4& 1\\
0 &6
\end{bmatrix}X=\begin{bmatrix}
\frac{-1}{4}& \frac{-1}{8}\\
0 &\frac{1}{6}
\end{bmatrix}\begin{bmatrix}
8& 9\\
24 &6
\end{bmatrix}$
$\begin{bmatrix}
1& -1\\
0 &1
\end{bmatrix}X=\begin{bmatrix}
-5& -3\\
4 &1
\end{bmatrix}$
$X=\begin{bmatrix}
-1& -2\\
4 &1
\end{bmatrix}$
