Part a
The system is NOT time-invariant
The general formulas for te system are:
x[n] = d[n-k]
y[n] = (k+1)^2 * d[n-(k+1)]
Shifting by a constant means that
x[n-a] = d[n-k-a]
y[n-a] = (k+1)^2 * d[n-(k+1)-a]
As seen from this procedure, when shifted the y[n-a] has a multiplying (k+1)^2 that does not yield the same value as in the nonshifted equation.
Part b
The input X[n] = u[n] will yield y[n] = u[n-1] because the system is linear.
