Inverting Matrices

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

Where I is the identity matrix.

A square matrix A has an inverse if the determinant . A matrix possessing an inverse is called nonsingular, or invertible.

The matrix inverse of a square matrix m may be taken in mathematics using the function inverse[m].

Inverse of 2x2 Matrix

For a 2X2  matrix

A= `[[a,b],[c,d]]`

The matrix inverse is

                  

             =  

                   =    

Inverse of 3x3 Matrix

For a 3X3 matrix

          

The matrix inverse is

A general matrix can be inverted using methods such as the gauss Jordan elimination, Gaussian elimination.