A unimodular matrix is a real square matrix A with determinant det(A) = ± 1. More generally, a matrix A with elements in the polynomial domain F[x] of a field F is called unimodular if it has an inverse whose elements are also in F[x]. A matrix A is therefore unimodular iff its determinant is a unit of F[x]. The matrix inverse of a unimodular real matrix is another unimodular matrix. There are an infinite number of 3×3 unimodular matrices not containing any 0s or ± 1. One parametric family is [8n^2 + 8n | 2n + 1 | 4n 4n^2 + 4n | n + 1 | 2n + 1 4n^2 + 4n + 1 | n | 2n - 1].

Chebyshev polynomial of the second kind | determinant | identity matrix | unit matrix