设矩阵 $H =\left[\begin{array}{lll}1 & 1 & 1 \\ 2 & 2 & 2 \\ 3 & 3 & 3\end{array}\right]$ ，则与 $H$ 相似的矩阵是（ ）。
A. $A =\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 2 & 0 \\ 0 & 0 & 0\end{array}\right]$
B. $B =\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 2 \\ 0 & 3 & 0\end{array}\right]$
C. $C =\left[\begin{array}{ccc}1 & 1 & 1 \\ a & a & a \\ -a & -a & -a\end{array}\right]$
D. $D =\left[\begin{array}{lll}1 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 1\end{array}\right]$