Part A
Can the system be time invariant?
Lets test and find out:
Part B
The system does a phase shift to the right by 1 unit and then multiplies the amplitude of the function by the square of total shift.
if Y[n] = u[n-1]
then in the function $ \delta[n-(k+1)] $ k must be equal to 0
we then multiply the amplitude by the square of the total shift (-1), which has no effect because it is the same as multiplying by 1.
We can finally solve and say that in order to produce Y[n], the input must be $ x(t) = u(t) $
