## 选项

[A].   $\left(\begin{array}{ll} \boldsymbol{A} & \boldsymbol{O} \\ \boldsymbol{C} & \boldsymbol{B} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll} \boldsymbol{A}^{-1} & \boldsymbol{O} \\ \boldsymbol{B}^{-1} \boldsymbol{C} \boldsymbol{A}^{-1} & \boldsymbol{B}^{-1} \end{array}\right)$

[B].   $\left(\begin{array}{ll} \boldsymbol{A} & \boldsymbol{O} \\ \boldsymbol{C} & \boldsymbol{B} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll} \boldsymbol{A}^{-1} & \boldsymbol{O} \\ -\boldsymbol{A}^{-1} \boldsymbol{C} \boldsymbol{B}^{-1} & \boldsymbol{B}^{-1} \end{array}\right)$

[C].   $\left(\begin{array}{ll} \boldsymbol{A} & \boldsymbol{O} \\ \boldsymbol{C} & \boldsymbol{B} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll} \boldsymbol{A}^{-1} & \boldsymbol{O} \\ -\boldsymbol{B}^{-1} \boldsymbol{C} \boldsymbol{A}^{-1} & \boldsymbol{B}^{-1} \end{array}\right)$

[D].   $\left(\begin{array}{ll} \boldsymbol{A} & \boldsymbol{O} \\ \boldsymbol{C} & \boldsymbol{B} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll} \boldsymbol{A}^{-1} & \boldsymbol{O} \\ -\boldsymbol{B} \boldsymbol{C}^{-1} \boldsymbol{A} & \boldsymbol{B}^{-1} \end{array}\right)$

$\left(\begin{array}{ll} \boldsymbol{\textcolor{orange}{A}} & \boldsymbol{O} \\ \boldsymbol{\textcolor{yellow}{C}} & \boldsymbol{\textcolor{cyan}{B}} \end{array}\right)^{\textcolor{red}{-1}}$ $=$ $\left(\begin{array}{ll} \boldsymbol{\textcolor{orange}{A}}^{\textcolor{red}{-1}} & \boldsymbol{O} \\ \textcolor{red}{-}\boldsymbol{\textcolor{cyan}{B}}^{\textcolor{red}{-1}} \boldsymbol{\textcolor{yellow}{C}} \boldsymbol{\textcolor{orange}{A}}^{\textcolor{red}{-1}} & \boldsymbol{\textcolor{cyan}{B}}^{\textcolor{red}{-1}} \end{array}\right)$

## 选项

[A].   $\left(\begin{array}{ll} \boldsymbol{A} & \boldsymbol{C} \\ \boldsymbol{O} & \boldsymbol{B} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll} \boldsymbol{A} & -\boldsymbol{A}^{-1} \boldsymbol{C} \boldsymbol{B}^{-1} \\ \boldsymbol{O} & \boldsymbol{B} \end{array}\right)$

[B].   $\left(\begin{array}{ll} \boldsymbol{A} & \boldsymbol{C} \\ \boldsymbol{O} & \boldsymbol{B} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll} \boldsymbol{A}^{-1} & -\boldsymbol{A}^{-1} \boldsymbol{C} \boldsymbol{B}^{-1} \\ \boldsymbol{O} & \boldsymbol{B}^{-1} \end{array}\right)$

[C].   $\left(\begin{array}{ll} \boldsymbol{A} & \boldsymbol{C} \\ \boldsymbol{O} & \boldsymbol{B} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll} \boldsymbol{A}^{-1} & -\boldsymbol{A} \boldsymbol{C}^{-1} \boldsymbol{B} \\ \boldsymbol{O} & \boldsymbol{B}^{-1} \end{array}\right)$

[D].   $\left(\begin{array}{ll} \boldsymbol{A} & \boldsymbol{C} \\ \boldsymbol{O} & \boldsymbol{B} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll} \boldsymbol{A}^{-1} & \boldsymbol{A}^{-1} \boldsymbol{C} \boldsymbol{B}^{-1} \\ \boldsymbol{O} & \boldsymbol{B}^{-1} \end{array}\right)$

$\left(\begin{array}{ll} \boldsymbol{\textcolor{orange}{A}} & \boldsymbol{\textcolor{yellow}{C}} \\ \boldsymbol{O} & \boldsymbol{\textcolor{cyan}{B}} \end{array}\right)^{\textcolor{red}{-1}}$ $=$ $\left(\begin{array}{ll} \boldsymbol{\textcolor{orange}{A}}^{-1} & \textcolor{red}{-}\boldsymbol{\textcolor{orange}{A}}^{\textcolor{red}{-1}} \boldsymbol{\textcolor{yellow}{C}} \boldsymbol{\textcolor{cyan}{B}}^{\textcolor{red}{-1}} \\ \boldsymbol{O} & \boldsymbol{\textcolor{cyan}{B}}^{-1} \end{array}\right)$

## 选项

[A].   $\left(\begin{array}{ll} \boldsymbol{O} & \boldsymbol{A} \\ \boldsymbol{B} & \boldsymbol{O} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{cc} \boldsymbol{O} & \boldsymbol{A^{-1}} \\ \boldsymbol{B^{-1}} & \boldsymbol{O} \end{array}\right)$

[B].   $\left(\begin{array}{ll} \boldsymbol{O} & \boldsymbol{A} \\ \boldsymbol{B} & \boldsymbol{O} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{cc} \boldsymbol{O} & \boldsymbol{B}^{\top} \\ \boldsymbol{A}^{\top} & \boldsymbol{O} \end{array}\right)$

[C].   $\left(\begin{array}{ll} \boldsymbol{O} & \boldsymbol{A} \\ \boldsymbol{B} & \boldsymbol{O} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{cc} \boldsymbol{O} & \boldsymbol{B}^{-1} \\ \boldsymbol{A}^{-1} & \boldsymbol{O} \end{array}\right)$

[D].   $\left(\begin{array}{ll} \boldsymbol{O} & \boldsymbol{A} \\ \boldsymbol{B} & \boldsymbol{O} \end{array}\right)^{-1}$ $=$ $\left(\begin{array}{cc} \boldsymbol{B}^{-1} & \boldsymbol{O} \\ \boldsymbol{O} & \boldsymbol{A}^{-1} \end{array}\right)$

$\left(\begin{array}{ll} \boldsymbol{O} & \boldsymbol{\textcolor{orange}{A}} \\ \boldsymbol{\textcolor{cyan}{B}} & \boldsymbol{O} \end{array}\right)^{\textcolor{red}{-1}}$ $=$ $\left(\begin{array}{cc} \boldsymbol{O} & \boldsymbol{\textcolor{cyan}{B}}^{\textcolor{red}{-1}} \\ \boldsymbol{\textcolor{orange}{A}}^{\textcolor{red}{-1}} & \boldsymbol{O} \end{array}\right)$

## 选项

[A].   $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{O} \\ \boldsymbol{O} & \boldsymbol{B}\end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll}\boldsymbol{O} & \boldsymbol{A}^{-1} \\ \boldsymbol{B}^{-1} & \boldsymbol{O}\end{array}\right)$

[B].   $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{O} \\ \boldsymbol{O} & \boldsymbol{B}\end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll}\boldsymbol{B}^{-1} & \boldsymbol{O} \\ \boldsymbol{O} & \boldsymbol{A}^{-1}\end{array}\right)$

[C].   $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{O} \\ \boldsymbol{O} & \boldsymbol{B}\end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll}-\boldsymbol{A} & \boldsymbol{O} \\ \boldsymbol{O} & -\boldsymbol{B}\end{array}\right)$

[D].   $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{O} \\ \boldsymbol{O} & \boldsymbol{B}\end{array}\right)^{-1}$ $=$ $\left(\begin{array}{ll}\boldsymbol{A}^{-1} & \boldsymbol{O} \\ \boldsymbol{O} & \boldsymbol{B}^{-1}\end{array}\right)$

$\left(\begin{array}{ll}\boldsymbol{\textcolor{orange}{A}} & \boldsymbol{O} \\ \boldsymbol{O} & \boldsymbol{\textcolor{cyan}{B}}\end{array}\right)^{\textcolor{red}{-1}}$ $=$ $\left(\begin{array}{ll}\boldsymbol{\textcolor{orange}{A}}^{\textcolor{red}{-1}} & \boldsymbol{O} \\ \boldsymbol{O} & \boldsymbol{\textcolor{cyan}{B}}^{\textcolor{red}{-1}}\end{array}\right)$

## 选项

[A].   $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{E}\end{array}\right)$ $\stackrel{\text {初等行变换}}{\longrightarrow}$ $\left(\begin{array}{ll}\boldsymbol{E} & – \boldsymbol{A}^{-1}\end{array}\right)$

[B].   $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{E}\end{array}\right)$ $\stackrel{\text {初等列变换}}{\longrightarrow}$ $\left(\begin{array}{ll}\boldsymbol{E} & \boldsymbol{A}^{-1}\end{array}\right)$

[C].   $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{E}\end{array}\right)$ $\stackrel{\text {初等行变换}}{\longrightarrow}$ $\left(\begin{array}{ll}\boldsymbol{E} & \boldsymbol{A}^{-1}\end{array}\right)$

[D].   $\left(\begin{array}{ll}\boldsymbol{A} & \boldsymbol{E}\end{array}\right)$ $\stackrel{\text {初等行变换}}{\longrightarrow}$ $\left(\begin{array}{ll} \boldsymbol{A}^{-1} & \boldsymbol{E}\end{array}\right)$

$\left(\begin{array}{ll}\boldsymbol{\textcolor{orange}{A}} & \boldsymbol{\textcolor{cyan}{E}}\end{array}\right)$ $\stackrel{\text {初等 [行] 变换}}{\longrightarrow}$ $\left(\begin{array}{ll}\boldsymbol{\textcolor{cyan}{E}} & \textcolor{yellow}{\boldsymbol{A}^{-1}}\end{array}\right)$

## 选项

[A].   $\boldsymbol{A}^{-1}$ $=$ $|\boldsymbol{A}|$ $\boldsymbol{A}^{*}$

[B].   $\boldsymbol{A}^{-1}$ $=$ $\frac{1}{|\boldsymbol{A}^{*}|}$ $\boldsymbol{A}$

[C].   $\boldsymbol{A}^{-1}$ $=$ $\frac{1}{|\boldsymbol{A}|}$ $\boldsymbol{A}^{*}$

[D].   $\boldsymbol{A}^{-1}$ $=$ $\frac{-1}{|\boldsymbol{A}|}$ $\boldsymbol{A}^{*}$

$\textcolor{orange}{\boldsymbol{A}^{-1}}$ $=$ $\frac{\textcolor{cyan}{1}}{\textcolor{green}{|\boldsymbol{A}|}}$ $\textcolor{red}{\boldsymbol{A}^{*}}$

## 选项

[A].   $\boldsymbol{A}^{-1}$ $=$ $- \boldsymbol{B}$

[B].   $\boldsymbol{A}^{-1}$ $=$ $\boldsymbol{B^{-1}}$

[C].   $\boldsymbol{A}^{-1}$ $=$ $\boldsymbol{B}$

[D].   $\boldsymbol{A}^{-1}$ $=$ $\boldsymbol{B B^{-1}}$

$\textcolor{orange}{\boldsymbol{A}^{-1}}$ $=$ $\textcolor{red}{\boldsymbol{B}}$

## 选项

[A].   $(\boldsymbol{A}+\boldsymbol{B})^{-1}$ $=$ $\boldsymbol{A}^{-1}$ $+$ $\boldsymbol{B}^{-1}$

[B].   $(\boldsymbol{A}+\boldsymbol{B})^{-1}$ $\neq$ $\boldsymbol{A}^{-1}$ $+$ $\boldsymbol{B}^{-1}$

$(\boldsymbol{\textcolor{orange}{A}}+\boldsymbol{\textcolor{orange}{B}})^{\textcolor{cyan}{-1}}$ $\textcolor{red}{\neq}$ $\boldsymbol{\textcolor{orange}{A}}^{\textcolor{cyan}{-1}}$ $+$ $\boldsymbol{\textcolor{orange}{B}}^{\textcolor{cyan}{-1}}$

## 选项

[A].   $\left|\boldsymbol{A}^{-1}\right|$ $=$ $|\boldsymbol{A}|$

[B].   $\left|\boldsymbol{A}^{-1}\right|$ $=$ $\frac{-1}{|\boldsymbol{A}|}$

[C].   $\left|\boldsymbol{A}^{-1}\right|$ $=$ $\frac{1}{|\boldsymbol{A}|}$

[D].   $\left|\boldsymbol{A}^{-1}\right|$ $=$ $\frac{1}{|\boldsymbol{A^{-1}}|}$

$\left|\boldsymbol{\textcolor{orange}{A}}^{\textcolor{cyan}{-1}}\right|$ $=$ $\frac{\textcolor{red}{1}}{|\boldsymbol{\textcolor{orange}{A}}|}$

## 选项

[A].   $\left(\boldsymbol{A}^{\mathrm{\top}}\right)^{-1}$ $=$ $\left(\boldsymbol{A}^{-1}\right)^{\mathrm{\top}}$

[B].   $\left(\boldsymbol{A}^{\mathrm{\top}}\right)^{-1}$ $=$ $\left(\boldsymbol{A}\right)^{\mathrm{\top}}$

[C].   $\left(\boldsymbol{A}^{\mathrm{\top}}\right)^{-1}$ $=$ $\left(\boldsymbol{A}^{\top}\right)^{\mathrm{\top}}$

[D].   $\left(\boldsymbol{A}^{\mathrm{\top}}\right)^{-1}$ $=$ $\left(\boldsymbol{A}^{-1}\right)^{\mathrm{-1}}$

$\left(\boldsymbol{\textcolor{orange}{A}}^{\mathrm{\textcolor{cyan}{\top}}}\right)^{\textcolor{red}{-1}}$ $=$ $\left(\boldsymbol{\textcolor{orange}{A}}^{\textcolor{red}{-1}}\right)^{\mathrm{\textcolor{cyan}{\top}}}$

[A].

[B].

## 选项

[A].   $(\boldsymbol{A B})^{-1}$ $=$ $(\boldsymbol{B A})^{-1}$

[B].   $(\boldsymbol{A B})^{-1}$ $=$ $-$ $\boldsymbol{B}$ $\boldsymbol{A}$

[C].   $(\boldsymbol{A B})^{-1}$ $=$ $\boldsymbol{A}^{-1}$ $\boldsymbol{B}^{-1}$

[D].   $(\boldsymbol{A B})^{-1}$ $=$ $\boldsymbol{B}^{-1}$ $\boldsymbol{A}^{-1}$

$(\boldsymbol{\textcolor{orange}{A} \textcolor{cyan}{B}})^{\textcolor{red}{-1}}$ $=$ $\boldsymbol{\textcolor{cyan}{B}}^{\textcolor{red}{-1}}$ $\boldsymbol{\textcolor{orange}{A}}^{\textcolor{red}{-1}}$

[A].

[B].

## 选项

[A].   $(k \boldsymbol{A})^{-1}$ $=$ $k$ $\boldsymbol{A}^{-1}$

[B].   $(k \boldsymbol{A})^{-1}$ $=$ $\frac{1}{k}$ $\boldsymbol{A}^{-1}$

[C].   $(k \boldsymbol{A})^{-1}$ $=$ $\frac{-1}{k}$ $\boldsymbol{A}^{-1}$

[D].   $(k \boldsymbol{A})^{-1}$ $=$ $\boldsymbol{A}^{-1}$

$(\textcolor{orange}{k} \boldsymbol{\textcolor{cyan}{A}})^{\textcolor{red}{-1}}$ $=$ $\textcolor{orange}{\frac{1}{k}}$ $\boldsymbol{\textcolor{cyan}{A}}^{\textcolor{red}{-1}}$

[A].

[B].