The @INVERSE function returns the inverse of matrix A. The syntax for @INVERSE:

AINV[, err] = @INVERSE( A);

where both AINV and A must be square and dense nxn matrices.

The optional argument, err, is an error flag that will be 0 if the invert operation was successful, otherwise it will be 1.  A situation where err would be nonzero is when A is a singular matrix.  If err is present, any error will be ignored by LINGO and will be left for your model to handle. If err is not present, then, on any error, LINGO will display an error message and terminate the run.

For more information, refer to the section Matrix Functions.