Inverting a vector If I have $Ax=b$ where $A$ is $n$ by $n$ while $x$ and $b$ are $n$ by 1, is it possible to find $A$ given $x$ and $b$. The idea would be some sort of $x^{-1}$ operation on the right of both equations but I'm not sure how to go about it. If necessary, we can consider a specific case of $n=2$.
Also, is the $A$ unique or not?

No, inverse in this case is impossible, because you have a lot of solutions, for example consider:
$A\begin{bmatrix} 1 \\ 0\end{bmatrix}=\begin{bmatrix} 1 \\ 0\end{bmatrix}$
$A=\begin{bmatrix}1 && 0 \\ 0 && 1\end{bmatrix}$is one solution, but for example $A=\begin{bmatrix}1 && 1 \\ 0 && 1\end{bmatrix}$ is solution, too.
