
                               In the first part, you have seen : 
 
 a)  You must copy into the identity matrix the inverse of the pivot value.
     Multiply this matrix by mA, the pivot value will be equal to 1.

 b)  You must copy all the values below the pivot in the identity matrix, and take the opposite.      Multiply this matrix by mA, the values below the pivot will be equal to 0.
 
                                 Can you do that in one step ?
                                 ===========================
         2/3  3/2  3/1  1/1
    mA = 2/1  1/4  1/3  1/2
         2/3  2/3  1/1  4/1
         3/1  2/3  1/2  1/2

1) You must copy all the values below the pivot in the identity matrix, and take the opposite. 

          1/1  0/1  0/1  0/1
  mID =  -2/1  1/1  0/1  0/1
         -2/3  0/1  1/1  0/1
         -3/1  0/1  0/1  1/1

2) Multiply all these values, plus, the pivot, by the inverse of the pivot value inv(2/3) = 3/2. 

         ( 1*3)/(2*1)  0/1  0/1  0/1
  mID =  (-2*3)/(2*1)  1/1  0/1  0/1
         (-2*3)/(2*3)  0/1  1/1  0/1
         (-3*3)/(2*1)  0/1  0/1  1/1

3) Now if you multiply this matrix by mA ...  
           
             1/1    9/4     9/2    3/2
 mID * mA =  0/1  -17/4   -26/3   -5/2
             0/1   -5/6    -2/1    3/1
             0/1  -73/12  -13/1   -4/1
