How to solve equation using inverse matrix method? I'm trying to solve the following equation:
$$
AX=B
$$
where
$A=\begin{bmatrix}1 & 5\\2 & 3\\-4 & 1\end{bmatrix}$, $B=\begin{bmatrix}1 & 2 & 5\\2 & 4 & 3\\-4 & -8 & -1\end{bmatrix}$
Usually I multiply both sides of the equation by $A^{-1}$ which results in $X=BA^{-1}$
However, matrix $A$ is not a square matrix so I cannot get its inverse. What I tried to do is multiply both sides of the equation by $B^{-1}$ and I get $AB^{-1}X=1$. But again I have no idea how to solve this.
Any tips on how to do this appreciated. Thx

Let 
$$X = \left[\begin{array}{ccc}a&b&c\\d&e&f\end{array}\right] $$
Then it should hold
$$\begin{array}{lrcl}
(1) & c+5f &=& 5 \\
(2) & 2c+3f&=&3 \\
(3) &-4c+f &=& -1
\end{array}$$
Then $(3)+2\cdot(2)$ reveals 
$$f = \frac{5}{7}$$
but $(3)+4\cdot(1)$ reveals that
$$f=\frac{19}{21}$$
a contradiction. Thus you system has no solution.
