(a)The system is time invariant
Let time delay = t
then
Xk[n]=δ[n-k] -> time delay -> system
equals to X(k+t)[n]=δ[n-(k+t)]->system
equals to X(k+t)[n]=δ[n-k-t]->system
equals to Y(k+t)[n]=$ (k+t+1)^2 $ δ[n-(k+t+1)]
while
Xk[n]=δ[n-k] -> system -> time delay
equals to Yk[n]=$ (k+1)^2 $ δ[n-(k+1)]->time delay
equals to Y(k+t)[n]=$ (k+t+1)^2 $ δ[n-(k+t+1)]
yields the same result
(b)
According to row 1 of the table, input x[n]=u[n] yields the output Y[n]=u[n-1].
