The image of the adjoint mapping Original Research Article

Let image be a commutative ring with 1, and let A be an m × n matrix over image with determinantal rank r greater-or-equal, slanted 1. If 1 is in ideal of image generated by the r × r minors of A, then every inner inverse of A is in the image of a linear mapping image that is specified in terms of the classical adjoints of the r × r submatrices of A.