Invertible Matrix Properties
Invertible matrices have various properties and some of the important properties of invertible matrices are listed below,
- Inverse can only be calculated for Square Matrix whose determinant is non.
- For the square matrix also the inverse of only the non-singular matrix exists. Non-singular matrices are the matrices where the determinant is non-zero.
- For any non-singular matrix A, (AT)-1 = (A-1)T where AT represents the Transpose matrix of A.
- For any two invertible matrices A and B, AB = In where In is the identity matrix.
- If the inverse of any matrix A exists then x = A-1B is the solution of the equation, Ax = B
- Det (A-1) = (Det A)-1
- (cA)-1 = 1/c.A-1
Invertible Matrix
Invertible matrices are defined as the matrix whose inverse exists. We define a matrix as the arrangement of data in rows and columns, if any matrix has m rows and n columns then the order of the matrix is m × n where m and n represent the number of rows and columns respectively.
We define invertible matrices as square matrices whose inverse exists. They are non-singular matrices as their determinant exists. There are various methods to calculate the inverse of the matrix.
In this article, we will learn about, What are Invertible Matrices? Invertible Matrices Examples, Invertible Matrix Theorems, Invertible Matrix Determinant, and others in detail.
Table of Content
- What is Invertible Matrix?
- Invertible Matrix Example
- Matrix Inversion Methods
- Invertible Matrix Theorem
- Invertible Matrix Properties
- Invertible Matrix Determinant
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