3x3 Matrix Inverse Calculator

The inverse of a matrix is something which can be very difficult to calculate and becomes more difficult when the order of the given matrix is 3 x 3.

3x3 Matrix Inverse Calculator
Matrix (A)
3x3 Matrix Inverse Calculator Results
Adjoint (adj A)
Determinant (|A|)
Inverse of Matrix = (adj A)/|A|

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3x3 Matrix Inverse Calculator. This image shows the properties and Matrix formula for the 3x3 Matrix Inverse Calculator

About the 3 x 3 matrix inverse calculator

The inverse of a matrix can only be found in the case if the matrix is a square matrix and the determinant of that matrix is a non-zero number. After that, you have to go through numerous lengthy steps, which are more time consuming in order to find the inverse of a matrix. Who would want to work so hard just to find out the inverse of a 3 x 3 matrix? This is the reason why iCalculator made this good online calculator that will save your manual calculations and save you a lot of time.

You can find out the inverse of a matrix (say A) by finding out the value of 'I' in the above equation: A = IA.

The use of this calculator is very easy. You just have to enter the values of the respective 3 x 3 order matrix in the required fields and hit the enter button. You will get the desired results immediately.

Calculating the inverse of a 3x3 matrix can be a daunting task, but with the help of our 3x3 Matrix Inverse Calculator, it's as easy as 1-2-3! In this tutorial, we'll guide you through the process of using our calculator step-by-step.

Step 1: Enter the Matrix

The first step is to enter your 3x3 matrix into the calculator. You can do this by typing the values of the matrix into the corresponding boxes. Make sure to enter the values in the correct order, starting with the top-left element and ending with the bottom-right element.

Step 2: Calculate the Determinant

The next step is to calculate the determinant of the matrix. You can do this by clicking the "Calculate" button next to the "Determinant" field. The determinant of a 3x3 matrix can be calculated using the following formula:

det(A) = a11(a22a33 - a32a23) - a12(a21a33 - a31a23) + a13(a21a32 - a31a22)

where A is the matrix, and aij represents the element in the ith row and jth column.

Step 3: Check for Invertibility

Before we calculate the inverse, we need to check if the matrix is invertible. A matrix is invertible if and only if its determinant is nonzero. If the determinant is zero, then the matrix is singular, and its inverse does not exist.

Step 4: Calculate the Adjoint

Assuming the matrix is invertible, we can now calculate the adjoint of the matrix. The adjoint of a matrix is obtained by taking the transpose of the matrix of cofactors. The cofactor of an element is obtained by multiplying its minor by (-1)^(i+j), where i and j are the row and column indices of the element. The minor of an element is obtained by deleting its row and column from the matrix and calculating the determinant of the resulting 2x2 matrix.

Step 5: Calculate the Inverse

Finally, we can calculate the inverse of the matrix using the formula:

A-1 = adj(A)/det(A)

where A-1 is the inverse of A, adj(A) is the adjoint of A, and det(A) is the determinant of A. You can calculate the inverse by clicking the "Calculate" button next to the "Inverse" field.

And there you have it! With our 3x3 Matrix Inverse Calculator, calculating the inverse of a 3x3 matrix has never been easier. Try it out for yourself and see how easy it is!

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