The specific steps are as follows: first, find the determinant value of matrix M, then express it as an auxiliary factor matrix, and multiply each item with the displayed symbol to get the inverse matrix.

1, the geometric meaning of matrix, invertible matrix is also called nonsingular matrix and full rank matrix, and the product of two invertible matrices is still invertible. The transposed matrix of invertible matrix is also invertible, and the matrix is invertible if and only if it is a full rank matrix.

2. The inverse matrix formula of matrix is a common tool in higher algebra, as well as in applied mathematics disciplines such as statistical analysis. In physics, matrices have applications in circuit science, mechanics, optics and quantum physics. In computer science, three-dimensional animation also needs matrix. Decomposition of a matrix into a combination of simple matrices can simplify the operation of the matrix in theory and practical application.

3. The property theorem of inverse matrix is still A. Write (a-1)-1= A. The transposed matrix at of reversible matrix A is also reversible, (AT)-1= (A- 1) "(The inversion of transposed matrix is equal to the inversion. That is, AB=O (or BA=O), then B=OAB=AC or (BA=CA), then b = C.

Matrix is a common tool in applied mathematics such as advanced algebra and statistical analysis. In physics, matrices have applications in circuit science, mechanics, optics and quantum physics. In computer science, three-dimensional animation also needs matrix. Matrix operation is an important problem in the field of numerical analysis.

Decomposition of a matrix into a combination of simple matrices can simplify the operation of the matrix in theory and practical application. For some widely used and special matrices, such as sparse matrix and quasi-diagonal matrix, there are concrete fast operation algorithms. For the development and application of matrix related theory, please refer to matrix theory.

Infinite-dimensional matrices will also appear in astrophysics, quantum mechanics and other fields, which is the generalization of matrices.