For most applications, the Gauss-Jordan method is an unnecessarily expensive way to do these computations. Our backslash operator (\), which indirectly finds the inverse and also solves linear systems, uses Gaussian elimination which is different than the Gauss-Jordan method. You can read more about the backslash operator within our documentation, shown at the following URL:
You can also use the RREF function to produce the reduced row echelon form of a matrix using Gauss Jordan elimination with partial pivoting.
