If the system of equations x−ky−z=0,kx−y−z=0,x+y−z=0 has a non-zero solution, then the possible values of k are

As the given system has a non-zero solution, 0=1−k−1k−1−111−1=1+k−k−1−11+k−2−100−1                   [Using C1→C1−C2,C2→C2+C3]⇒ 0    =(−1)[(1+k)(−2)−(1+k)(−k−1)]⇒ 0    =(1+k)(−2+k+1)⇒k=−1,1