Inverse 2×2 matrix online

Do you need calcular la matriz inversa 2x2 online to save time? Use our calculator and you will be able to get the inverse matrix automatically in a matter of seconds, step by step.

To do this, you must write down each of the elements that make up the matriz inversa 2x2 y pulsar el botón de calcular cuando lo hayas hecho. Tras eso, conocerás el resultado y los pasos previos que conlleva a este cálculo como son el determinante 2x2 y la matriz adjunta.

Fórmula para calcular matriz inversa 2x2

Formula for calculating inverse matrix

If you want to hallar la matriz inversa 2x2 or of size nxn by the method of attachments, you can use the formula that heads this theoretical point.

As mentioned above, in order to calcular la matriz inversa 2x2 you need to know:

  • Calcular el determinante 2x2 de la matriz
  • Calculate the adjoint matrix and then draw its transpose.

Por último, la matriz inversa 2x2 será el resultado de dividir cada elemento de la transpuesta de la matriz adjunta entre el valor del determinante.

Remember that the first thing you must do is to calculate the determinant because in case it comes out to be zero, the matrix will have no inverse and the problem will be over.

Example of inverse matrix

Example of a 3x3 matrix

Let's see how to calculate the inverse matrix of the example a partir de la teoría que acabamos de contarte. En este caso, la matriz es de orden 3 pero si lo que quieres es hallar la inversa de una matriz 2x2, el procedimiento es exactamente el mismo o incluso más fácil, ya que es más pequeña y tiene menos elementos.

1 - Calculamos el determinante

3x3 determinant

To know if the matrix has an inverse or not, the first thing to do is to solve its determinant. If the result is non-zero as in this case, we will go to the next point to solve the inverse of a matrix.

If you do not know cómo se resuelve el determinante de una matriz 2x2We recommend that you click on the link we have left for you and in which we explain in detail how it is done.

2 - Sacar matriz adjunta

The following step to calculate the inverse matrix of the example consists of drawing the attached matrix. Here what we have to do is to choose one by one all the elements of the matrix, in such a way that we cancel its column and row to form a determinant that has to be solved and placed in its position.

In addition, a rule of signs must be observed that you have represented in the following figure and that dictates the places where we will have to place a plus or minus sign according to the position of each element of the matrix.

Matrix-4x4-assemblies

Applying all of the above to our example, we are left with the following calculations for each of the elements of the adjoining matrix:

Calculation of attachments

Finally, we group all the results and we are left with the following attached matrix that we will use for the next step:

Attached matrix

3 - Transpuesta de la matriz adjunta

Once the attached matrix has been calculated in the previous step, transposing it will take only a few seconds. To do so, we have to exchange rows for columns as shown below:

Matrix transposed from the attached

4 - Aplicar la fórmula para hallar la matriz inversa

Now we go back and copy the formula that we saw in the first section of this article for draw the inverse matrix. We substitute, solve the operations and we will have something like this:

Inverse matrix

In the event that you have to calcular la matriz inversa 2x2, el procedimiento es exactamente igual than the one in this example but much simpler since we have fewer elements and, therefore, fewer operations to perform.

Hallar matriz inversa 2x2 con Excel

Inverse matrix 2x2

Excel te permite calcular la matriz inversa 2x2 The system is very easy to use, as it incorporates a specific function for this purpose.

Just follow the steps below and you will be able to calculate any inverse matrix nxn with Excel:

  1. Escribe la matriz 2x2 en una hoja de cálculo de Excel vacía
  2. Busca un rango de celdas 2x2 vacío, selecciónalo y escribe la siguiente fórmula, además, recuerda que entre los paréntesis irá el rango de celdas en el que has escrito la matriz para la cual quieres hallar su inversa.

=MINVERSE()

  1. Press the CTRL + Shift keys on your keyboard and without releasing them, press ENTER to confirm your selection. Excel formula to calculate the inverse matrix.

If the process has been done correctly, you will instantly see the result.

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