已知矩阵 $\boldsymbol{A}=\left(\begin{array}{lll}a & a & b \\ a & b & a \\ b & a & a\end{array}\right)(a b \neq 0)$ 的正、负惯性指数相同，则 $\boldsymbol{A}$ 相似于
A. $\left(\begin{array}{ccc}a & 0 & 0 \\ 0 & -a & 0 \\ 0 & 0 & 0\end{array}\right)$
B. $\left(\begin{array}{ccc}2 a & 0 & 0 \\ 0 & -2 a & 0 \\ 0 & 0 & 0\end{array}\right)$
C. $\left(\begin{array}{ccc}3 a & 0 & 0 \\ 0 & -3 a & 0 \\ 0 & 0 & 0\end{array}\right)$
D. $\left(\begin{array}{ccc}4 a & 0 & 0 \\ 0 & -4 a & 0 \\ 0 & 0 & 0\end{array}\right)$