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?