<s>[INST] Solve a matrix equation I need to find $X$ from 
$$\begin{pmatrix}
1 & 2\\ 
-3 &-6 
\end{pmatrix} X \begin{pmatrix}
1 &2 \\ 
-1 &-2 
\end{pmatrix}=\begin{pmatrix}
2 &4 \\ 
-6 & -12
\end{pmatrix}$$
I wrote $X$ as 
$$X=\begin{pmatrix}
a & b\\ 
c &d 
\end{pmatrix}$$
and I got $a+2c-b-2d=2$ but I do not know what to do next. Please help.
 [/INST] You are on good way. When you multiply matrices on left side, you finally get $$a-b+2c-2d = 2$$ which is a linear equation. Solutions are given with three parameters, and thus
$$ X = \begin{pmatrix}
a & b\\
c & \frac{a-b+2c-2}{2}
\end{pmatrix}$$
</s>