The determinant of the inverse of an invertible matrix is the inverse of the determinant: det(A-1) = 1 / det(A) [6.2. 6, page 265]. Similar matrices have the same determinant; that is, if S is invertible and of the same size as A then det(S A S-1) = det(A).
What does inverting a matrix do to its determinant?
It holds that det(AB)=det(A)det(B), so that det(A)det(A−1)=1. In other words, an invertible matrix has (multiplicatively) invertible determinant. (If you work over a field, this means just that the determinant is non-zero.)
How do you find the determinant of an inverse matrix?
The inverse of a matrix can be calculated by following the given steps:
- Step 1: Calculate the minor for the given matrix.
- Step 2: Turn the obtained matrix into the matrix of cofactors.
- Step 3: Then, the adjugate, and.
- Step 4: Multiply that by reciprocal of determinant.
