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Unimodular matrix

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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 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 × n general linear group over Z {\displaystyle \mathbb {Z} } , which is denoted GL n ⁡ ( Z ) {\displaystyle \operatorname {GL} _{n}(\mathbb {Z} )} .