AHSME 1973 Problem 10

If $n$ is a real number, then the simultaneous system $nx+y = 1$ $ny+z = 1$ $x+nz = 1$ has no solution if and only if $n$ is equal to $\textbf{(A)}\ -1 \textbf{(B)}\ 0 \textbf{(C)}\ 1 \textbf{(D)}\ 0\text{ or }1 \textbf{(E)}\ \frac{1}2$