The inverse of a square matrix A, denoted by A^{-1}, is the matrix so that AA^{-1} = I, where I is the Identity matrix.

The LAPACK routines that compute matrix inverses are in the form of xyyTRI, categorized into the Computational routines. The matrix inverse routines require factoriztion (LU, Cholesky, etc.) and more operations than the solve routines, and they may demand extra workspace.