code: public InvertibleMatrix inverse() throws MatrixException
      {
          InvertibleMatrix inverse  = new InvertibleMatrix(nRows);
          IdentityMatrix   identity = new IdentityMatrix(nRows);
  
          // Compute each column of the inverse matrix
          // using columns of the identity matrix.
          for (int c = 0; c < nCols; ++c) {
              ColumnVector col = solve(identity.getColumn(c), true);
              inverse.setColumn(col, c);
          }
  
          return inverse;
      }
docs: Compute the inverse of this matrix.
  @return the inverse matrix
  @throws matrix.MatrixException if an error occurred