Determinant of Inverse Matrix
Determinant of inverse matrix is the reciprocal of the determinant of the original matrix. i.e.,
det(A-1) = 1 / det(A)
The proof of the above statement is discussed below:
det(A × B) = det (A) × det(B) (already know)
⇒ A × A-1 = I (by Inverse matrix property)
⇒ det(A × A-1) = det(I)
⇒ det(A) × det(A-1) = det(I) [ but, det(I) = 1]
⇒ det(A) × det(A-1) = 1
⇒ det(A-1) = 1 / det(A)
Hence, Proved.
Inverse of a Matrix
The inverse of Matrix is the matrix that on multiplying with the original matrix results in an identity matrix. For any matrix A, its inverse is denoted as A-1.
Let’s learn about the Matrix Inverse in detail, including its definition, formula, methods on how to find the inverse of a matrix, and examples.
Table of Content
- Matrix Inverse
- Terms Related to Matrix Inverse
- How to Find Inverse of Matrix?
- Inverse of a Matrix Formula
- Inverse Matrix Method
- Inverse of 2×2 Matrix Example
- Determinant of Inverse Matrix
- Properties of Inverse of Matrix
- Matrix Inverse Solved Examples