What is Inverse of a Matrix?
Inverse of a Matrix is defined as the matrix when multiplied by the original matrix gives the identity matrix. If A is a matrix, then the inverse of matrix A is represented as A-1. The inverse of a matrix can only be determined for a square matrix and the determinant is not equal to zero (i.e., non-singular matrix).
Inverse of a Matrix Definition
The matrix results in identify matrix when multiplied by the given matrix A then the matrix is called as Inverse matrix of A. It is denoted as A-1.
AA-1 = A-1A = I
where,
- A-1 is Inverse of Matrix A
- I is an Identity Matrix
Methods to Find Inverse of a Matrix
Methods to find the inverse of a matrix involve the inverse of a matrix formula and by elementary operations. The inverse of matrix A is represented as A-1 which when multiplied by matrix A gives an identity matrix.
In this article, we will explore different methods to find the inverse of a matrix in detail along with the inverse of matrix definition and inverse of matrix properties.
Table of Content
- What is Inverse of a Matrix?
- Inverse of a Matrix Definition
- Properties of Inverse of Matrix
- Methods to Find Inverse of a Matrix
- Inverse of a Matrix by Inverse of Matrix Formula
- Steps to Find Inverse of Matrix by Inverse of Matrix Formula
- Inverse of Matrix by Elementary Transformations
- Inverse of 2 × 2 Matrix
- Examples of Methods to Find Inverse of a Matrix
- Practice Problems on Methods to Find Inverse of a Matrix
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