Suppose that $A$ is a square matrix of size $n\times n$ and that we know there is a single vector $\vect{b}\in\complex{n}$ such that the system $\linearsystem{A}{\vect{b}}$ has a unique solution. Prove that $A$ is a nonsingular matrix. (Notice that this is very similar to Theorem NMUS, but is not exactly the same.)