Inverse 3×3 matrix online

Calcula la matriz inversa 3x3 online step by step with our calculator that will allow you to find the inverse of a matrix instantly.

Sólo tienes que rellenar correctamente todos los valores que componen la matriz 3x3 y pulsar sobre el botón de calcular para obtener el resultado paso a paso  cómo se ha calculado su matriz inversa a partir de la fórmula que veremos más adelante. Descubre cómo se calcula la inversa de una matriz 3x3.

Fórmula para calcular la matriz inversa 3x3 y nxn

Formula for calculating inverse matrix

Para calcular la inversa de una matriz 3x3, 4x4 o del tipo nxn, sólo tienes que aplicar la fórmula que tienes encima de estas líneas.

In the formula to calculate the inverse matrix we can see that we have to calculate:

  • The determinant of the starting matrix nxn
  • Transpose the attached matrix

Cuando tengamos ambos datos, hacemos la división correspondiente y obtendremos la matriz inversa 3x3 o la del tipo nxn que busquemos.

Ejemplos de matriz inversa 3x3

Example of a 3x3 matrix

Let's take a practical example cómo calculamos la matriz inversa 3x3 that we have just put.

1 - Calcular determinante de matriz 3x3

3x3 determinant

As we have said in the previous point, the first thing we must do in order to sacar la matriz inversa 3x3 is calculate the determinant of the matrix.

When we have the result of the determinant, two things can happen:

  • Si el valor del determinante 3x3 is equal to zero, then there is no inverse matrix.
  • If the determinant has a non-zero heat, we can calculate its inverse.

2 - Calcular matriz adjunta

Now let's calculate the attached matrix and to do so, we must eliminate the row and the column in which each element of the matrix is located. With the remaining elements we will form a determinante 2x2 to be solved. This must be done with each and every one of the elements that form the matrix.

In addition, you must remember that the attached matrix has a specific order of symbols associated with each of the positions of the matrix as shown in the following figure:


Based on our example, it remains that the step by step to calculate the attached matrix is as follows:

Calculation of attachments

Once we group the results obtained by calculating the adjoint determinant of each element of the matrix, we are left with the following matriz adjunta 3x3 is as follows:

Attached matrix

3 - Transponemos la matriz adjunta

This step is very fast, because in order to make the transpose of the adjoining matrixIn the table below, we only have to exchange rows for columns. This leaves us with the following result:

Matrix transposed from the attached

4 - Aplicamos la fórmula para sacar la matriz inversa 3x3

The fourth and final step is to apply the fórmula para calcular la matriz inversa 3x3 we saw above.

We copy it, compile the results obtained in the previous operations and solve.

Example of 3x3 inverse matrix

Cómo sacar la matriz inversa 3x3 en Excel

Calculate 3x3 inverse matrix

If you want to make your own calculadora de matriz inversa 3x3 con ExcelYou can get it in a very simple way if you follow these steps:

  1. Abre una nueva hoja de cálculo y escribe en ella la matriz 3x3 para la cual quieres calculate its inverse.
  2. Cuando la tengas escriba, busca un rango 3x3 de celdas vacías y selecciónalo. Cuando lo tengas, escribe la siguiente función de Excel que te permitirá calcular la matriz inversa 3x3 (recuerda que entre los paréntesis irá el rango de celdas 3x3 en los que has escrito tu matriz):


  1. Now press simultaneously the CTRL + Shift keys on your keyboard and without releasing, press the ENTER key to accept the formula. If you have done it right, Excel calculará la matriz inversa 3x3 automatically.

If you have any doubts about the procedure to follow, we recommend you to watch the video and you will find out. If you still have any doubts, leave us a comment and we will try to help you as soon as possible.

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