$$
\text { 设 } n \text { 阶矩阵 } A=\left(\begin{array}{ccccc}
1 & a & a & \cdots & a \\
a & 1 & a & \cdots & a \\
a & a & 1 & \cdots & a \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
a & a & a & \cdots & 1
\end{array}\right), n \geq 3 \text { 且 }
$$
$r(A)=n-1$, 则 $a=$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$