Matrix inverse calculator

  About matrix inverse calculator

This is a free online matrix inverse calculator using Cofactor, Gauss-Jordan, Gaussian elimination, Montante(Bareiss algorithm) with complete, detailed, step-by-step description of solutions, that performs operations with matrices up to 99x99 in size with matrix elements of this type: decimal numbers, fractions, complex numbers, variables.

To start the calculation, you need to first enter the size of the matrix in the input field that you can find from the very top of the screen, also there you can choose the desired method of calculation.

A little below you will find a matrix window in which you need to enter matrix elements using the keyboard. The matrix control panel is also located here, which simplifies work with matrices and contains the following control elements:

• The first element allows you to expand the matrix window. This can be especially useful in cases where you need to perform calculations with very large matrices that do not fit completely. If the matrix is still not visible after expanding the window, you can change the scale of the matrix using the + / - buttons;
• The second element performs the function of copying the matrix input to the memory buffer. This can be useful in cases where you often use the same matrix for calculations, or if you need to move matrices between operations;
• And the last element inserts the previously copied matrix, which allows you to speed up the process of entering the matrix to just a few clicks, instead of doing it manually;

And further down you will find a toolbar that allows you to customize the calculator and make it easier to work with it. It is visually divided into three parts, each of which is responsible for the following functionality:

• The first allows you to select the number format when the solution result is displayed. Also, here you can turn off comments to the solution of the problem if you have already understood how to solve this problem, and you use the calculator to speed up or check your own calculations. Or you can turn off the step-by-step solution entirely if you only need the result of the solution;
• The second contains buttons that allow you to change the type of the matrix input field, erase its elements or the entire matrix, and the largest button with an equal sign, which will take you to the screen with the solution of the problem. All these buttons are duplicated by keys on the keyboard. To find out which key on the keyboard to press, simply hover over one of the buttons and a tooltip will appear with the name of the key. You can also use the arrow keys on your keyboard to move the cursor between matrix input fields;
• And the last one allows you to choose the number of digits after the decimal point for rounding non-integer numbers. Also, here you can immediately see an example of how rounded fractions will look;

  What is the inverse of a matrix(matrix to the -1 power)?

If we take any number and divide one by that number, we find the reciprocal, which is the inverse of that number, and if we multiply that number by its reciprocal, we get one. Like ordinary numbers have reciprocal, square matrices can have an inverse matrix if their determinant is not equal to zero, otherwise these matrices are considered singular and it is impossible to find an inverse matrix for them. And if we multiply the matrix by its inverse matrix, we will get an identity matrix as a result. Identity matrix is a matrix that behaves with other matrices in the similar way that the number one behaves with other numbers, when we multiply any matrix by the identity matrix, we will get the same matrix as a result. In the identity matrix on the main diagonal, elements are equal one, and all other elements are equal to zero.

  How to find the inverse of a matrix using the Cofactor?

To find the inverse of a matrix using the cofactor, first need to find the determinant of this matrix, and if it is zero, it is impossible to find the inverse of such a matrix. If the determinant is not zero, we can continue the calculation, and first we have to find the minor of the matrix, then the cofactor of the matrix, and then the adjugate matrix. Now we need to divide one by the determinant and multiply it by each element of the adjugate matrix, and the result will be the inverse matrix.

  How to find the inverse of a matrix using Gauss-Jordan?

To find the inverse of a matrix using the Gauss-Jordan method, we can add an identity matrix of the same size to the right of the matrix. After that, if we apply the Gauss-Jordan method to such a matrix in such a way that an identity matrix is formed on the left, then on the right we get the inverse.

  How to find the inverse of a matrix using Gaussian elimination?

To find the inverse of a matrix using Gaussian elimination, we can add an identity matrix of the same size to the right of the matrix. After that, if we apply Gaussian elimination to such a matrix in such a way that an identity matrix is formed on the left, then on the right we get the inverse.

  How to find the inverse of a matrix using Montante(Bareiss algorithm)?

To find the inverse of a matrix using Bareiss algorithm, we can add an identity matrix of the same size to the right of the matrix. After that, if we apply Bareiss algorithm to such a matrix in such a way that an identity matrix is formed on the left, then on the right we get the inverse.