Inverse Matrix – Definition, Method, Example, and Properties

# Inverse Matrix – Definition, Method, Example, and Properties

## Inverse Matrix – Introduction

Inverse Matrix is a mathematical operation that calculates the inverse of a given matrix. The inverse matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix. The inverse matrix is unique, if it exists.

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## Matrix Inverse

A matrix inverse is a matrix that, when multiplied by the original matrix, produces the identity matrix. There are various methods for computing a matrix inverse, but the most common is the Gauss-Jordan Method.

## Rank of the Matrix

The rank of a matrix is the number of linearly independent columns or rows in the matrix.

## Inverse Matrix Formula

Inverse Matrix Formula

The inverse matrix formula calculates the inverse of a given matrix. The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix.

## Methods to Find Inverse of Matrix

Inverse Matrix Method

To find the inverse matrix of a given matrix, we use the following steps:

1. Find the determinant of the matrix.

2. If the determinant is zero, the matrix is not invertible and cannot be inverted.

3. If the determinant is not zero, the inverse matrix can be found using the inverse matrix formula.

4. Invert the matrix.

5. Check the inverse matrix to make sure it is correct.

## How are we Going to Measure the Inverse?

There are a few ways to measure the inverse. One way is to use a calculator. Another way is to use a coordinate plane.

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