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I'm a bit confused. Based on Wikipedia:

In mathematics, a unimodular matrix M is a square integer matrix having determinant +1, 0 or −1. Equivalently, it is an integer matrix that is invertible over the integers.

So determinant could be +1, 0 or −1. But a matrix is invertible only if determinat is non-zero! In fact, from Wolfram:

A unimodular matrix is a real square matrix A with determinant det(A) = -1|+1.

Which is right answer?

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The Wikipedia article must be wrong. Hopefully someone who knows about unimodular matrices will fix it. – littleO Nov 11 '12 at 10:57
@littleO thank you a lot. – user34295 Nov 11 '12 at 11:06
up vote 4 down vote accepted

Well spotted. In a case like this, it's a good idea to check the article's history (using the "View history" link at the top). In the present case, the error was introduced only two days ago by an anonymous user in this edit (which I just reverted).

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Fine. So the right answer is det(A) is -1 or +1 (unimodular matrix) while in a totally unimodular matrix every square non-singular matrix in unimodular. Is the bold part actually needed? – user34295 Nov 11 '12 at 13:24
@Gremo: It is -- if you look at the examples in the Wikipedia article: many of the matrices there have zero entries. – joriki Nov 11 '12 at 13:45

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