✔ 最佳答案
To prove that det(A)*det(B) = det(AB) Iwould suggest to use the 3 basic operations that can be done by matrix multiplication:
1. Switch two rows(or columns) - negates the determinants sign.
2. Multiplying a row(or a column) by a scalar - multiply the determinant by that scalar.;
3. Adding a row multiplied by a scalar to another row - no change.
Every square matrix is a product of those elementart matrix, and the product of their determinants is the determinant of their product.
1=det(I) = det(A * A^-1) = det(A)*det(A^-1)
Multiply by det(A)^-1 and you'll get
det(A)^-1 = det(A^-1)