In this paper, the generalized orthogonal solutions of the matrix inverse problem AX = B and associated optimal approximation problem are considered. The properties and structure of generalized orthogonal matrices are given, the relationship between the generalized orthogonal matrices and the orthogonal matrices are discussed. Necessary and sucient conditions for the solvability of the matrix inverse problem AX = B, the general expression of solutions, and its procrustes problem are discussed. In addition, the corresponding optimal approximation solutions are presented. Finally, the algorithms and corresponding computational examples are given.