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I'm a bit confused about the definition of a totally unimodular matrix, since my lecture notes states that this matrix is not totally unimodular:

$$\begin{pmatrix} 1 && 0 \\ 1 && -1 \\ -2 && 1 \end{pmatrix}$$

I don't see a submatrix which doesn't have a determinant in $\lbrace 0,\pm1 \rbrace$. What am I doing wrong?

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From Schrijver's Theory of Linear and Integer Programming (1998):

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Note that $-2 \notin \{-1,0,1\}$.

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    Ah, the wiki page didn't seem to mention this. Maybe I overlooked smt, or we're just dealing with different definitions. Thanks anyway, I guess your answer is correct, since Schrijver's book indeed is pensum for this class. Thanks! – 2017-01-31