## Introduction to Matrix Adjoint Calculator

The adjoint matrix calculator is an online free tool used to calculate the adjoint of a matrix. It interchanges the diagonal values and signs to find the adjoint of a 2-by-2 square matrix. It uses the cofactor method for a square matrix of order greater than 2-by-2.

In matrix algebra, the adjoint of a matrix is the most used method because it is used for the calculated inverse of a matrix. The adjoint of a matrix of order 2-by-2 is easier than the greater orders. You can calculate it easily by hand. But for a greater order matrix, finding adjoint becomes tricky and lengthy. We introduce a tool that can calculate the adjoint of any matrix of any order.

## Formula used by Adjoint of a Matrix Calculator

The adjoint of a matrix is the transpose of its cofactor matrix. There are two ways to calculate adjoint, 1st is for a square matrix of order 2 and the 2nd is for the square matrix of order greater than 2.

**Let A be a general matrix of order 2×2,**

$$ A \;=\; \begin{bmatrix} a & b \\ c & d \\ \end{bmatrix} $$

Then the adjoint of this matrix is,

$$ adjA \;=\; \begin{bmatrix} -d & -b \\ -c & a \\ \end{bmatrix} $$

**Let A be a 3×3 matrix,**

$$ A \;=\; \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{bmatrix} $$

The adjoint of this matrix is,

$$ adjA \;=\; \begin{bmatrix} A_{11} & A_{12} & A_{13} \\ A_{21} & A_{22} & A_{23} \\ A_{31} & A_{32} & A_{33} \\ \end{bmatrix}^T $$

Where,

$$ A_{11},A_{12},A_{13},A_{21},…….A_{ij} $$

are the cofactors of matrix A.

The cofactors of A can be calculated by the following formula:

$$ A_{ij} \;=\; (-1)^{i+j} \; det(M_{ij}) $$

M_{ij} are the minors of the matrix A.

The above formulas are used by the adjoint calculator.

## Why use a Cofactor Matrix Calculator?

In matrix algebra, the adjoint of a matrix is the necessary condition to find the inverse matrix. The adjoint of a square matrix of order 2 is easy to calculate, but the transpose of cofactors is necessary for higher-order. It is a lengthy and time-consuming procedure, but you can get the solution quickly if you use the matrix adjoint calculator with steps. It is an efficient way to solve a problem using this tool.

## How to use an Adjoint Matrix Calculator?

It is easy to calculate and find the adjoint of a matrix with the adjoint calculator because it has simple and easy steps to be performed. These steps are:

- First, you need to enter the number of rows and columns for a matrix.
- Enter the values of all matrix entries in the given format of the matrix.
- You can also use the random button for any random matrix selected by the tool.
- Click on the calculate button.

The cofactor calculator executes according to the given order of the matrix. So, you will get the solution within a few moments.

## Benefits of using Adjoint Matrix Step by Step Calculator

The calculatores.com site offers many math tools that are helpful for students and mathematicians. These tools do not only solve the given problem but also give a step-by-step solution to clear concepts. The adjoint of a matrix calculator with steps has many beneficial uses that make it more reliable for you. These benefits are:

- Adjoint matrix calculator with steps can solve adjoints for any matrix according to its order.
- It can handle up to 4 order square matrices efficiently.
- Cofactor matrix calculator can save you from calculating cofactors, which is a lengthy procedure.
- It is a free tool, so you can use it anytime and anywhere without paying any fee.
- Matrix adjoint calculator also helps you to clear your concept by providing a step-by-step solution.