  By using the quasi-determinant the construction of Gel'fand et al. leads to
the inverse of a matrix with noncommuting entries. In this work we offer a new
method that is more suitable for physical purposes and motivated by deformation
quantization, where our constructed algorithm emulates the commutative case and
in addition gives corrections coming from the noncommutativity of the entries.
Furthermore, we provide an equivalence of the introduced algorithm and the
construction via quasi-determinants.
