$2 n$ 阶行列式 $D_{2 n}=\left|\begin{array}{ll}\boldsymbol{A} & \boldsymbol{B} \\ \boldsymbol{B} & \boldsymbol{A}\end{array}\right|=$ $\_\_\_\_$ ，其中 $n$ 阶矩阵

$$
\boldsymbol{A}=\left[\begin{array}{cccc}
a & 0 & \cdots & 0 \\
0 & a & \cdots & 0 \\
\vdots & \vdots & & 0 \\
0 & 0 & \cdots & a
\end{array}\right], \quad \boldsymbol{B}=\left[\begin{array}{cccc}
0 & \cdots & 0 & b \\
0 & \cdots & b & 0 \\
\vdots & & \vdots & \vdots \\
b & \cdots & 0 & 0
\end{array}\right] .
$$