NCInverse[aSquareMatrix]

Aliases: None.

Description: NCInverse[$m$] gives a symbolic inverse of a matrix with noncommutative entries.

Arguments: $m$ is an $n \times n$ matrix with noncommutative entries.

Comments / Limitations: This command is primarily used symbolically and is not guarenteed to work for any specific examples. Usually the elements of the inverse matrix ($m^{-1}$) are huge expressions. We recommend using NCSimplifyRational[NCInverse[$m$]] to improve the formula you get. In some cases, NCSimplifyRational[$m^{-1} m$] does not provide the identity matrix, even though it does equal the identity matrix. The formula we use for NCInverse[] comes from the LDU decomposition. Thus in principle it depends on the order chosen for pivoting even if the inverse of a matrix is unique.