If I have these matrix relationship expressed as a factorization:
$$\mathbf{A}=\mathbf{B}\cdot\mathbf{C}$$
where they are $\mathbf{A}\in\{0, 1\}^{m , n}$, $\mathbf{B}\in\{0, 1\}^{m , r}$ and $\mathbf{C}\in\{0, 1\}^{r , n}$.
What if I know $\mathbf{A}$ and $\mathbf{C}$ and I want to solve for $\mathbf{B}$? I suppose that the solution is not unique, how can I get several different values for $\mathbf{B}$ that satisfy the factorization?
I'd rather not involve pseudo-inverses (supposing I could use them)