Calculate the inverse 3×3 matrix online step by step with our calculator that will allow you to find the inverse of a matrix instantly.
Just fill in correctly all the values that compose the 3×3 matrix and click on the calculate button to get the result step by step how its inverse matrix has been calculated from the formula we will see below. Discover how to calculate the inverse of a 3×3 matrix.
Formula for calculating the inverse matrix 3×3 and nxn
To calculate the inverse of a 3×3, 4×4 or nxn type matrix, just apply the formula above these lines.
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
When we have both data, we make the corresponding division and we will obtain the inverse 3×3 matrix or the one of the nxn type we are looking for.
Examples of 3×3 inverse matrix
Let's take a practical example how to calculate the inverse 3×3 matrix that we have just put.
1 - Calculate determinant of 3×3 matrix
As we have said in the previous point, the first thing we must do in order to to draw the inverse 3×3 matrix is calculate the determinant of the matrix.
When we have the result of the determinant, two things can happen:
- If the value of the determinant 3×3 is equal to zero, then there is no inverse matrix.
- If the determinant has a non-zero heat, we can calculate its inverse.
2 - Calculate adjoining matrix
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 2×2 determinant 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:
Once we group the results obtained by calculating the adjoint determinant of each element of the matrix, we are left with the following attached 3×3 matrix is as follows:
3 - We transpose the attached matrix
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:
4 - We apply the formula to obtain the inverse matrix 3×3
The fourth and final step is to apply the formula to calculate the inverse matrix 3×3 we saw above.
We copy it, compile the results obtained in the previous operations and solve.
How to extract the inverse 3×3 matrix in Excel
If you want to make your own 3×3 inverse matrix calculator with ExcelYou can get it in a very simple way if you follow these steps:
- Open a new spreadsheet and write in it the 3×3 matrix for which you want to calculate its inverse.
- When you have it written, find a 3×3 range of empty cells and select it. When you have it, type the following Excel function that will allow you to calculate the inverse 3×3 matrix (remember that between the parentheses will be the range of 3×3 cells in which you have written your matrix):
- 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 will calculate the inverse matrix 3×3 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.