已知向量组 $\alpha_1=\left(\begin{array}{c}1 \\ 0 \\ -1 \\ -1\end{array}\right), \alpha_2=\left(\begin{array}{c}1 \\ -1 \\ 0 \\ -2\end{array}\right), \alpha_3=\left(\begin{array}{c}0 \\ -1 \\ 1 \\ -1\end{array}\right), \alpha_4=\left(\begin{array}{c}0 \\ 1 \\ -1 \\ 1\end{array}\right)$ ，记 $A=\left(\alpha_1, \alpha_2, \alpha_3, \alpha_4\right)$ ，$$
G=\left(\alpha_1, \alpha_2\right)
$$

（1）证明：$\alpha_1, \alpha_2$ 是 $\alpha_1, \alpha_2, \alpha_3, \alpha_4$ 的极大线性无关组．
（2）求矩阵 $H$ 使得 $A=G H$ ，并求 $A^{10}$ ．