计算$2n$阶行列式 $\left|\begin{array}{cccccc}
a & 0 & 0 & \cdots & 0 & b \\
0 & a & 0 & \cdots & b & 0 \\
0 & 0 & a & \cdots & 0 & 0 \\
\cdots & \cdots & \cdots & \cdots \cdots \cdots & \cdots \cdots & \\
0 & b & 0 & \cdots & a & 0 \\
b & 0 & 0 & \cdots & 0 & a
\end{array}\right|$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$
$\text{E.}$
$\text{F.}$