a=var('a')
b=var('b')
c=var('c')
A=matrix([[1,a,a*a],[1,b,b*b],[1,c,c*c]])
A.add_multiple_of_row(2,0,-1)
A.add_multiple_of_row(1,0,-1)
A.rescale_row(1,(c-a))
A.rescale_row(2,(b-a))
A.add_multiple_of_row(2,1,-1)
print A
print A[0,0]*A[1,1]*A[2,2]