1.
Under which one of the following conditions does the system of equations
{kx+y+z=k1x+ky+z=k1x+y+kz=k1\begin{cases} kx + y + z = k - 1 \\ x + ky + z = k - 1 \\ x + y + kz = k - 1 \end{cases}

have a unique solution?