设 $\boldsymbol{A}$ 为三阶实对称矩阵, $\boldsymbol{A}$ 的秩 $r(A)=2$ ,且
$$
A\left(\begin{array}{cc}
1 & 1 \\
0 & 0 \\
-1 & 1
\end{array}\right)=\left(\begin{array}{cc}
-1 & 1 \\
0 & 0 \\
1 & 1
\end{array}\right) \text {. }
$$
(1)求 $\boldsymbol{A}$ 的特征值与特征向量;
(2)求矩阵 $\boldsymbol{A}$.
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$