Solve $ UA = B$, given $A$ and $B$

Solve $ UA = B$, given $A$ and $B$

If I have $A = \begin{bmatrix}1 \\0\end{bmatrix}$ and $B =
\begin{bmatrix}0 \\1\end{bmatrix}$
I want a matrix $U$ that will transform $A$ to $B$, for example $U =
\begin{bmatrix}0 & 1 \\1 & 0\end{bmatrix}$ will work, but how can I
algorithmically work out $U$ in general?