Inverse matrix calculator

The calculator below computes the inverse matrix via the Gauss-Jordan algorithm. You can find theory and formulas under the calculator.

Inverse of a matrix

-1 2 5 3 4 6 -8 2 12

Source matrix

Calculation precision

Digits after the decimal point: 2

Calculate

Inverse of a matrix

 

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The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix such that

For manual calculation you can use adjugate matrix to compute matrix inverse like this:

Adjugate matrix is the transpose of the cofactor matrix of A.

Cofactor of of A is defined as

where is a minor of .

You can use this method relatively easily for small matrices, 2x2, 3x3, or, maybe, 4x4. For bigger matrices, it is easier to use the Gauss-Jordan algorithm implemented by the calculator.