Matrices over centrally \(\mathbb Z_2\)-graded rings (Q1856588)

The authors introduce a new computational technique for \(n\times n\) matrices over a \(\mathbb{Z}_2\)-graded ring \(R=R_0\oplus R_1\) with \(R_0\subseteq Z(R)\), leading to a new concept of the determinant which can be used to derive an invariant Cayley-Hamilton identity. An explicit construction of the inverse matrix \(A^{-1}\) for any invertible \(n\times n\) matrix \(A\) over a Grassmann algebra \(E\) is also obtained.