Abstract: The matrix is one of the main linear algebra study, linear algebra plays an important role in the matrix theory is very rich in content, can be said that the main line of linear algebra. It is to learn mathematics and other subjects (such as numerical analysis, optimization theory, probability and statistics, operations research, control theory, electronics, information science, management science and engineering) are the basis of scientific and engineering computing a powerful tool. Invertible matrix theory is a very important concept, the reversible nature of Matrix Inversion Method and Application of naturally we have to study to become one of the main. This article first presents the concept of reversible matrix, nature, equivalent characterization of invertible matrices by discussing the nature and equivalent conditions, given some applications of inverse matrix and the inverse matrix Invertible Matrix Method, and an example for analysis.
Key words: reversible matrix; adjoint matrix; elementary transformation; inverse matrix; Cramer rule; matrix equation.