I'm trying to solve a matrix equation problem and I can't work out the correct form for the equation for it to be valid.
The matrices given are:
A= $\begin{bmatrix} 1 & -1 & 3\\ 4 & 1 & 5\\ 0 & 0 & 0\\ \end{bmatrix}$, B= $\begin{bmatrix} 1 & -1\\ 3 & 6\\ 1 & 0\\ \end{bmatrix}$, C= $\begin{bmatrix} -1 & 0\\ 5 & 6\\ 0 & 1\\ \end{bmatrix}$
The equation goes as follows: $AX + B = C - X$
I arrange it to: $X= (C - B)*(A+I)^{-1}$ via the following steps: $$AX + B = C - X$$ $$AX +X = C - B$$ $$X(A+I) = C - B /(A+I)^{-1}$$ $$X = (C - B) (A+I)^{-1}$$
But the problem is that the matrices $(C-B)$ and $(A+I)^{-1}$ can't be multiplied because they're not chained (the number of rows and collumns don't allow multiplication). I've been looking at this for over half an hour and can't figure out a different approach. Any help would be highly appreciated.
$X=(A+I)^{-1}(C-B )=\begin{bmatrix}\frac14 &\frac18 &\frac{-11}{8}\\\frac{-1}{2} &\frac14 &\frac14\\0 &0 &1\end{bmatrix}\begin{bmatrix}-2 &1\\2 &0\\-1 &1\end{bmatrix}=\begin{bmatrix}\frac98 &\frac{-9}{8}\\\frac54 &\frac{-1}{4}\\-1 &1\end{bmatrix}$
We get two independent solutions for $X$.