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, you need $n$ independent vectors $x$ to find $A$, in which case you would have one expression of $A$ in the base of you vectors $x_1,...x_n$.
