Unimodular matrix

In mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix N which is its inverse (these are equivalent under Cramer's rule). Thus every equation Mx = b, where M and b are both integer, and M is unimodular, has an integer solution. The unimodular matrices of order n form a group, which is denoted G L n ( Z ) {displaystyle GL_{n}(mathbb {Z} )} . Unimodular matrices form a subgroup of the general linear group under matrix multiplication, i.e. the following matrices are unimodular: