试求行列式 $|\boldsymbol{A}|,|\boldsymbol{B}|,|\boldsymbol{C}|$ ，其中 $\boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}$ 分别为 $n, m, n+m$ 阶方阵：

$$
\begin{aligned}
\boldsymbol{A} & =\left[\begin{array}{cccc}
1+x & 1 & \cdots & 1 \\
1 & 1+x & \cdots & 1 \\
\vdots & \vdots & & \vdots \\
1 & 1 & \cdots & 1+x
\end{array}\right], \\
\boldsymbol{B} & =\left[\begin{array}{cccc}
0 & \cdots & 0 & 1 \\
0 & \cdots & 2 & 0 \\
\vdots & & \vdots & \vdots \\
m & \cdots & 0 & 0
\end{array}\right], \boldsymbol{C}=\left[\begin{array}{cc}
\mathbf{0} & \boldsymbol{A} \\
\boldsymbol{B} & \mathbf{0}
\end{array}\right] .
\end{aligned}
$$