The calculator below computes inverse matrix via Gauss-Jordan algorithm. Some theory and formulas can found 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 easy for small matrices, 2x2, 3x3, or, may be, 4x4. For bigger matrices it is easier to use Gauss-Jordan algorithm implemented by calculator.