1. In a $3 \times 3$ square grid, fill in the numbers as shown in the table below. The operation on the table is as follows: each operation involves adding a number to two adjacent numbers in the grid (adjacent means two small squares that share a common edge).
\begin{tabular}{|l|l|l|}
\hline 0 & 3 & 2 \\
\hline 6 & 7 & 0 \\
\hline 4 & 9 & 5 \\
\hline
\end{tabular}

Can it be done after several operations such that
(1) all the numbers in the grid are 0;
(2) the numbers in the four corners are all 1, and the rest are 0.
(Tip: (1) After 5 operations, all cells can be 0.
(2) As shown in the table below, the invariant $S=a-$ $b+c-d+e-f+g-h+k$.
\begin{tabular}{|l|l|l|}
\hline$a$ & $b$ & $c$ \\
\hline$d$ & $e$ & $f$ \\
\hline$g$ & $h$ & $k$ \\
\hline
\end{tabular}

The initial state is
$$
S=0-3+2-6+7-0+4-9+5=0,
$$

The target state is
$$
S=1-0+1-0+0-0+1-0+1=4 \text {. }
$$

Therefore, it is impossible.)