a)Time-Invariant?
It is almost trivial to show that the system is time-invariant because all it does is time shift and magnitude scale the input (there is no frequency scaling). If the input itself is shifted, this same shift will appear in the output. The same result could be obtained by shifting the output instead of the input. This is, by definition, time-invariance.
b)Input to Output
$ X[n]=\:? \longrightarrow Y[n]=u[n-1] $
