(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].

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