Unimodular matrix

In mathematics, a unimodular matrixM is a squareinteger matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix N that is its inverse (these are equivalent under Cramer's rule). Thus every equation Mx = b, where M and b both have integer components and M is unimodular, has an integer solution. The n × n unimodular matrices form a group called the n × ngeneral linear group over ${\displaystyle \mathbb {Z} }$, which is denoted ${\displaystyle \operatorname {GL} _{n}(\mathbb {Z} )}$.