# Unimodular matrix definition?

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.

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