## Introduction to Adjoint Matrix Calculator:

The adjoint matrix calculator is a great tool for **evaluating the adjoint**, or adjugate of a given matrix. It is used to find the adjoint of a square matrix A using the cofactor matrix transpose method.

Our matrix adjoint calculator is a helpful tool for students, teachers, or professionals who can evaluate adjoint matrix solutions with just one click and a few seconds.

## What is Adjoint of a Matrix?

Adjoint of a matrix is a process in which you take the **transpose of cofactor** matrix elements in linear algebra. The adjoint can be represented with A^T; here, t denotes the transpose of a matrix. It is also known as an adjoint or adjugate matrix.

Although it is a very easy method to find an adjoint matrix, if you know about the matrix basis, especially the cofactor or determinant, you can find the adjoint without any difficulty in manual calculation.

## How to Calculate Adjoint of a Matrix?

To find the adjoint of a matrix, you should know about the cofactor **determinant method** and the transpose of a matrix basis.

Nevertheless, you do not need to worry; we will explain the whole process of finding the adjoint of a matrix with the help of an example of a stepwise process.

Suppose a matrix A. Find the adjoint of the matrix.

$$ A \;=\; \left[ \begin{matrix} 6 & 0 & 1 \\ 3 & 8 & 9 \\ 1 & 4 & 2 \\ \end{matrix} \right] $$

**Solution:**

$$ Adj(A) \;=\; Adj \left[ \begin{matrix} 6 & 0 & 1 \\ 3 & 8 & 9 \\ 1 & 4 & 2 \\ \end{matrix} \right] $$

Find the cofactor of each element using the minor method.

$$ \left[ \begin{matrix} + \biggr| \begin{matrix} 8 & 9 \\ 4 & 2 \\ \end{matrix} \biggr| & - \biggr| \begin{matrix} 3 & 9 \\ 1 & 2 \\ \end{matrix} \biggr| & + \biggr| \begin{matrix} 3 & 8 \\ 1 & 4 \\ \end{matrix} \biggr| \\ - \biggr| \begin{matrix} 0 & 1 \\ 4 & 2 \\ \end{matrix} \biggr| & + \biggr| \begin{matrix} 6 & 1 \\ 1 & 2 \\ \end{matrix} \biggr| & - \biggr| \begin{matrix} 6 & 0 \\ 1 & 4 \\ \end{matrix} \biggr| \\ + \biggr| \begin{matrix} 0 & 1 \\ 8 & 9 \\ \end{matrix} \biggr| & - \biggr| \begin{matrix} 6 & 1 \\ 3 & 9 \\ \end{matrix} \biggr| & + \biggr| \begin{matrix} 6 & 0 \\ 3 & 8 \\ \end{matrix} \biggr| \end{matrix} \right] $$

Solve all the determinants of all the cofactors of a matrix,

$$ =\; \left[ \begin{matrix} + (8 \times 2 - 9 \times 4) & - (3 \times 2 - 9 \times 1) & + (3 \times 4 - 8 \times 1) \\ -(0 \times 2 - 1 \times 4) & +(6 \times 2 - 1 \times 1) & -(6 \times 4 - 0 \times 1) \\ +(0 \times 9 - 1 \times 8) & -(6 \times 9 - 1 \times 3) & +(6 \times 8 - 0 \times 3) \\ \end{matrix} \right] $$

$$ \left[ \begin{matrix} + (16 - 36) & - (6 - 9) & + (12 - 8) \\ -(0 - 4) & +(12 - 1) & -(24 + 0) \\ +(0 - 8) & -(54 - 3) & +(48 - 3) \\ \end{matrix} \right] $$

After finding the determinate, the new matrix becomes,

$$ \left[ \begin{matrix} -20 & 3 & 4 \\ 4 & 11 & -24 \\ -8 & -51 & 48 \\ \end{matrix} \right] $$

Find the transpose of the above matrix,

$$ \left[ \begin{matrix} -20 & 3 & 4 \\ 4 & 11 & -24 \\ -8 & -51 & 48 \\ \end{matrix} \right]^{T} $$

Therefore, the solution of adjoint matrix A is,

$$ \left[ \begin{matrix} -20 & 4 & -8 \\ 3 & 11 & -51 \\ 4 & -24 & 48 \\ \end{matrix} \right] $$

To skip the manual process and calculate the adjoint of a matrix instantly with step-by-step solutions, try our free matrix adjoint calculator.

## How to Use Adjoint of a Matrix Calculator?

The adjoint matrix calculator has a simple design that helps everyone to solve the given matrix adjoint question instantly. You need to put your problem in it and follow some important instructions to get results without any hassle. These instructions are:

- Choose the size of the matrix that is given in the input box to find the adjoint of the matrix.
- Enter the elements of the matrix that you want to get the solution of the adjoint matrix in the input fields.
- Review your given input value to get the exact solution of the adjoint matrix question.
- The Calculate button evaluates the example of matrix adjoint problems.
- If you want to check the workings behind our adjoint of 3x3 matrix calculator, you can use the load example and its solution to learn more about this concept.
- Click the “
**Recalculate**” button for the evaluation of more examples of the adjoint matrix with the solution.

## What Outcome Adjoint of Matrix Calculator Give?

The adjoint of a matrix calculator provides you with a **solution** per your input problem when you click the calculate button. It may include the following:

**In the Result Box,**

Click on the result button to get the solution to your adjoint matrix question.

**Steps Box**

When you click on the steps option, you get the solution to the adjoint matrix questions step-by-step.

## Useful features of Adjoint Calculator:

The adjoint of a matrix calculator has many useful features. It allows you to solve adjoint matrix problems and get their solutions immediately.

Our tool only gives the input value and provides a solution without manual calculation. These features are:

- It is a
**reliable tool**as it always provides you with accurate solutions of the given matrix into an adjoint matrix - The adjoint of 3x3 matrix calculator is an efficient tool that provides solutions in the form of adjoint matrices from the given matrix problems in a few seconds.
- It is a learning tool that provides you with complete information about the concept of adjoint matrix very easily through online platforms.
- Adjoint matrix calculator is a free tool that allows you to use it for the calculation of adjoint matrix without taking a fee.
- It is a handy tool that solves adjoint matrix problems quickly without external effort.
- Adjoint of matrix calculator is an easy-to-use tool; anyone or even a beginner can easily use it for the solution of matrix adjoint problems.