问题
已知，$\boldsymbol{E}$ 为单位矩阵，则根据可逆矩阵的性质，以下利用 初 等 变 换 法 求逆矩阵的方法表述中，正确的是哪个？选项
[A]. $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{E}\end{array}\right)$ $\stackrel{\text {初等行变换}}{\longrightarrow}$ $\left(\begin{array}{ll} \boldsymbol{A}^{-1} & \boldsymbol{E}\end{array}\right)$[B]. $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{E}\end{array}\right)$ $\stackrel{\text {初等行变换}}{\longrightarrow}$ $\left(\begin{array}{ll}\boldsymbol{E} & – \boldsymbol{A}^{-1}\end{array}\right)$
[C]. $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{E}\end{array}\right)$ $\stackrel{\text {初等列变换}}{\longrightarrow}$ $\left(\begin{array}{ll}\boldsymbol{E} & \boldsymbol{A}^{-1}\end{array}\right)$
[D]. $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{E}\end{array}\right)$ $\stackrel{\text {初等行变换}}{\longrightarrow}$ $\left(\begin{array}{ll}\boldsymbol{E} & \boldsymbol{A}^{-1}\end{array}\right)$
$\left(\begin{array}{ll}\boldsymbol{\textcolor{orange}{A}} & \boldsymbol{\textcolor{cyan}{E}}\end{array}\right)$ $\stackrel{\text {初等 [行] 变换}}{\longrightarrow}$ $\left(\begin{array}{ll}\boldsymbol{\textcolor{cyan}{E}} & \textcolor{yellow}{\boldsymbol{A}^{-1}}\end{array}\right)$
