Inverse 2×2 matrix online

Do you need calculate the inverse 2×2 matrix 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 2×2 inverse matrix and click the calculate button when you have done it. After that, you will know the result and the previous steps involved in this calculation such as the 2×2 determinant and the adjoint matrix.

Formula for calculating 2×2 inverse matrix

Formula for calculating inverse matrix

If you want to find the inverse 2×2 matrix 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 calculate the inverse 2×2 matrix you need to know:

  • Calculate the 2×2 determinant of the matrix
  • Calculate the adjoint matrix and then draw its transpose.

Finally, the inverse 2×2 matrix will be the result of dividing each element of the transpose of the attached matrix by the value of the determinant.

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 from the theory we have just told you. In this case, the matrix is of order 3 but if you want to find the inverse of a 2×2 matrix, the procedure is exactly the same or even easier, since it is smaller and has fewer elements.

1 - Calculate the determinant

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 how to solve the determinant of a 2×2 matrixWe recommend that you click on the link we have left for you and in which we explain in detail how it is done.

2 - Draw attached matrix

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.


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 - Transpose of the adjoining matrix

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 - Apply the formula to find the inverse matrix

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 to calculate the inverse 2×2 matrix, the procedure is exactly the same than the one in this example but much simpler since we have fewer elements and, therefore, fewer operations to perform.

Finding 2×2 inverse matrix with Excel

Inverse matrix 2x2

Excel allows you to calculate the inverse 2×2 matrix 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. Write the 2×2 matrix in an empty Excel spreadsheet
  2. Find an empty 2×2 range of cells, select it and type the following formula, also remember that between the parentheses will be the range of cells in which you have typed the matrix for which you want to find its inverse.


  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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