一般情况下，$(\boldsymbol{A} \boldsymbol{B})^{\textcolor{cyan}{k}}$ $\textcolor{red}{\neq}$ $\boldsymbol{A}^{\textcolor{cyan}{k}}$ $\boldsymbol{B}^{\textcolor{cyan}{k}}$
$\left(\boldsymbol{A}^{\textcolor{orange}{k}}\right)^{\textcolor{cyan}{l}}$ $=$ $\boldsymbol{A}^{\textcolor{orange}{k} \textcolor{cyan}{l}}$
$\boldsymbol{A}^{\textcolor{orange}{k}}$ $\boldsymbol{A}^{\textcolor{cyan}{l}}$ $=$ $\boldsymbol{A}^{\textcolor{orange}{k} \textcolor{yellow}{+} \textcolor{cyan}{l}}$
$\boldsymbol{A}^{3}$ $=$ $\boldsymbol{A}$ $\cdot$ $\boldsymbol{A}$ $\cdot$ $\boldsymbol{A}$
由 $\boldsymbol{A B}$ $=$ $\boldsymbol{O}$, 不能推出 $\boldsymbol{A}$ $=$ $\boldsymbol{O}$ 或 $\boldsymbol{B}$ $=$ $\boldsymbol{O}$
当 $\boldsymbol{A}$ $\neq$ $\boldsymbol{O}$ 时，由 $\boldsymbol{A B}$ $=$ $\boldsymbol{A C}$ 不能推出 $\boldsymbol{B}$ $=$ $\boldsymbol{C}$
已知 $a$ 为常数，计算如下定积分：
$$
\int \frac{1}{a^{2} + x^{2}} \mathrm{d} x
$$
$\boldsymbol{A}$ $\boldsymbol{B}$ $\neq$ $\boldsymbol{B}$ $\boldsymbol{A}$
$\boldsymbol{\textcolor{orange}{E}}$ $\boldsymbol{\textcolor{cyan}{A}}$ $=$ $\boldsymbol{A}$ $\boldsymbol{\textcolor{orange}{E}}$ $=$ $\boldsymbol{\textcolor{cyan}{A}}$
$\boldsymbol{\textcolor{cyan}{C}}$ $\textcolor{orange}{(}$ $\boldsymbol{\textcolor{yellow}{A}}$ $+$ $\boldsymbol{\textcolor{yellow}{B}}$ $\textcolor{orange}{)}$ $=$ $\boldsymbol{\textcolor{cyan}{C} \textcolor{yellow}{A}}$ $+$ $\boldsymbol{\textcolor{cyan}{C} \textcolor{yellow}{B}}$
$\textcolor{orange}{(}$ $\boldsymbol{\textcolor{yellow}{A}}$ $+$ $\boldsymbol{\textcolor{yellow}{B}}$ $\textcolor{orange}{)}$ $\boldsymbol{\textcolor{cyan}{C}}$ $=$ $\boldsymbol{\textcolor{yellow}{A} \textcolor{cyan}{C}}$ $+$ $\boldsymbol{\textcolor{yellow}{B} \textcolor{cyan}{C}}$
$\textcolor{cyan}{\lambda}$ $\textcolor{orange}{(}$ $\boldsymbol{A B}$ $\textcolor{orange}{)}$ $=$ $\textcolor{orange}{(}$ $\textcolor{cyan}{\lambda}$ $\boldsymbol{A}$ $\textcolor{orange}{)}$ $\boldsymbol{B}$ $=$ $\boldsymbol{A}$ $\textcolor{orange}{(}$ $\textcolor{cyan}{\lambda}$ $\boldsymbol{B}$ $\textcolor{orange}{)}$
$\textcolor{orange}{(}$ $\boldsymbol{A B}$ $\textcolor{orange}{)}$ $\boldsymbol{C}$ $=$ $\boldsymbol{A}$ $\textcolor{orange}{(}$ $\boldsymbol{B C}$ $\textcolor{orange}{)}$
则，$\boldsymbol{A} \boldsymbol{B}$ $=$ $?$
$\boldsymbol{A} \boldsymbol{B}$ $=$ $\begin{bmatrix} 3 & 2\\ 1 & 0 \end{bmatrix}$
$3$ $=$ $1$ $\textcolor{orange}{\times}$ $3$ $\textcolor{cyan}{+}$ $(-1)$ $\textcolor{orange}{\times}$ $0$ $\textcolor{cyan}{+}$ $0$ $\textcolor{orange}{\times}$ $1$
$2$ $=$ $1$ $\textcolor{orange}{\times}$ $1$ $\textcolor{cyan}{+}$ $(-1)$ $\textcolor{orange}{\times}$ $(-1)$ $\textcolor{cyan}{+}$ $0$ $\textcolor{orange}{\times}$ $2$
$1$ $=$ $0$ $\textcolor{orange}{\times}$ $3$ $\textcolor{cyan}{+}$ $2$ $\textcolor{orange}{\times}$ $0$ $\textcolor{cyan}{+}$ $1$ $\textcolor{orange}{\times}$ $1$
$0$ $=$ $0$ $\textcolor{orange}{\times}$ $1$ $\textcolor{cyan}{+}$ $(-1)$ $\textcolor{orange}{\times}$ $2$ $\textcolor{cyan}{+}$ $1$ $\textcolor{orange}{\times}$ $2$
则，$\boldsymbol{A} \boldsymbol{B}$ 运算所得的矩阵 $\boldsymbol{C}$ 是一个几行几列的矩阵？
$\textcolor{orange}{m}$ 行 $\textcolor{cyan}{s}$ 列
