Given matrices $A$ and $B$, solve $XA = B$ 
Let $$A = \begin{bmatrix} 3&-7\\ 1&-2\end{bmatrix} \qquad \qquad B = \begin{bmatrix} 0&3\\ 1&-5\end{bmatrix}$$ and $X$ be an unknown $2x2$ matrix.
a. Find $A^{-1}$ 
b. If $XA = B$, use (a) to find $X$.

I found
$$A^{-1} = \begin{bmatrix} -2&7\\ -1&3\end{bmatrix}$$
I am stuck on the part b. I thought that if $XA=B$, then
$$X=A^{-1}B$$
so I did:
$$ X=
 \left[
\begin{array}{cc}
  -2&7\\
  -1&-3
\end{array}
\right]
 \left[
\begin{array}{cc}
  0&3\\
  1&-5
\end{array}
\right] $$
and got:
$$X = 
 \left[
\begin{array}{cc}
  7&-41\\
  3&-18
\end{array}
\right] $$
I have been told that this is not correct and I missed a technical detail of matrix multiplication. Please help.

The problem with your answer lies in the fact that what we actually have is$$XA=B\iff X=BA^{-1}.$$
