Where a * is the adjoint matrix of matrix a.

2. Elementary transformation method: carry out elementary transformation on (a, e), transform A into unit array E, and transform identity matrix E into A- 1.

Let a be an n-order matrix in the number field, and if there is another n-order matrix b in the same number field, it makes:? AB=BA=E？ Then we call B the inverse matrix of A and A the invertible matrix. Note: E is identity matrix.

Extended data:

Properties of invertible matrices;

1, the invertible matrix must be a square matrix.

2. If matrix A is invertible, its inverse matrix is unique.

3. the inverse matrix of the inverse matrix of a is still a, and write (a-1)-1= a.

4. The transpose mATrix at of invertible matrix A is also invertible, (AT)- 1=(A- 1)T? (The inverse of transposition is equal to the reverse transposition).

5. If matrix A is invertible, then matrix A satisfies the elimination law. That is, AB=O (or BA=O), then B=O, AB=AC (or BA=CA), then b = C.

6. The product of two invertible matrices is still invertible.

7. A matrix is invertible if and only if it is a full rank matrix.