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