Determining if the system is linear and time invariant
Hint : Use following properties of Discrete-Time Fourier Transform :


If $DTFT\{x[n]\} = X(e^{j\omega})$, then $DTFT\{x[n - n_0]\} = e^{-j\omega n_0}X(e^{j\omega})$
$IDTFT\{j\frac{\partial{}}{\partial\omega}X(e^{j\omega})\} = n x[n]$