(Using matrices) Determine the values of k so that the following system has: i) a unique solution

1. (Using matrices) Determine the values of k so that the following system has:
   i) a unique solution
   ii) no solution
   iii) an infinite number of solutions

kx + y + z = 1
x + ky + z = 1

x + y + kz = 1

Normally the "k" is only on one line or one colum which makes it easy to eliminate it by row reduction. In this case, no matter how many elementary row operations I try, I just get a bigger mess of "k"s.