For unimodular matrices this is the case. It seems reasonable that this is also the case for totally unimodular matrices, but I couldn't find a reference for this.
Does someone know why it is true or false?
2026-03-25 09:50:09.1774432209
Is the product of two totally unimodular matrices again totally unimodular?
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this is false. totally unimodular matrices have -1, 0 and 1 coefficients only, and by squaring a simple $2\times 2$ matrix you can get a counter example.
$$\left(\begin{matrix}1 & 1\\1 & 0\end{matrix}\right)^2 = \left(\begin{matrix}2 & 1\\1 & 1\end{matrix}\right) $$