问题
已知，矩阵 $\boldsymbol{A}$ $=$ $\begin{bmatrix} 1 & -1 & 0\\ 0 & 2 & 1 \end{bmatrix}$, 矩阵 $\boldsymbol{B}$ $=$ $\begin{bmatrix} 3 & 1\\ 0 & -1\\ 1 & 2 \end{bmatrix}$.则，$\boldsymbol{A} \boldsymbol{B}$ $=$ $?$
选项
[A]. $\boldsymbol{A} \boldsymbol{B}$ $=$ $\begin{bmatrix} 4 & 0\\ 0 & 1 \end{bmatrix}$[B]. $\boldsymbol{A} \boldsymbol{B}$ $=$ $\begin{bmatrix} 3 & 2\\ 1 & 0 \end{bmatrix}$
[C]. $\boldsymbol{A} \boldsymbol{B}$ $=$ $\begin{bmatrix} 4 & 2\\ 7 & 5 \end{bmatrix}$
[D]. $\boldsymbol{A} \boldsymbol{B}$ $=$ $\begin{bmatrix} 4 & 1\\ -1 & 1\\ 1 & 3 \end{bmatrix}$
$\boldsymbol{A} \boldsymbol{B}$ $=$ $\begin{bmatrix} 3 & 2\\ 1 & 0 \end{bmatrix}$
$3$ $=$ $1$ $\textcolor{orange}{\times}$ $3$ $\textcolor{cyan}{+}$ $(-1)$ $\textcolor{orange}{\times}$ $0$ $\textcolor{cyan}{+}$ $0$ $\textcolor{orange}{\times}$ $1$
$2$ $=$ $1$ $\textcolor{orange}{\times}$ $1$ $\textcolor{cyan}{+}$ $(-1)$ $\textcolor{orange}{\times}$ $(-1)$ $\textcolor{cyan}{+}$ $0$ $\textcolor{orange}{\times}$ $2$
$1$ $=$ $0$ $\textcolor{orange}{\times}$ $3$ $\textcolor{cyan}{+}$ $2$ $\textcolor{orange}{\times}$ $0$ $\textcolor{cyan}{+}$ $1$ $\textcolor{orange}{\times}$ $1$
$0$ $=$ $0$ $\textcolor{orange}{\times}$ $1$ $\textcolor{cyan}{+}$ $(-1)$ $\textcolor{orange}{\times}$ $2$ $\textcolor{cyan}{+}$ $1$ $\textcolor{orange}{\times}$ $2$