A unimodular matrix $M$ is a square integer matrix having determinant $+1$ or $−1$. A totally unimodular matrix (TU matrix) is a matrix for which every square non-singular submatrix is unimodular. A totally unimodular matrix need not be square itself. Obviously, any totally unimodular matrix has only $0$, $+1$ or $−1$ entries.

Now suppose a $n\times n$ non-singular matrix $A$ is totally unimodular. Can we prove that $A^{-1}$ is also totally unimodular? Or if it is not correct, can we have a counterexample?