
 The matrix mA :

            -2,5,  1,1,  2,1,
       mA =  3,2,  3,4,  3,1,
             4,1,  2,1,  1,2,

 If you copy into the identity matrix
 the inverse of the pivot value,
 of a matrix mA :  

             -5/2  0/1  0/1       
       mID =  0/1  1/1  0/1          
              0/1  0/1  1/1        

 And now if you multiply this matrix, 
 by mA for example, the pivot value
 will be  equal to 1.
             
             1/1  -5/2  -5/1
 mID * mA =  3/1   3/4   3/1
             4/1   2/1   1/2

    

