证明 $n$ 阶矩阵
$$
A=\left(\begin{array}{cccc}
1 & 1 & \cdots & 1 \\
1 & 1 & \cdots & 1 \\
\vdots & \vdots & & \vdots \\
1 & 1 & \cdots & 1
\end{array}\right) \text { 与 } B=\left(\begin{array}{cccc}
0 & \cdots & 0 & 1 \\
0 & \cdots & 0 & 2 \\
\vdots & & \vdots & \vdots \\
0 & \cdots & 0 & n
\end{array}\right)
$$

相似.