题目内容

设`\n`阶方阵`\A`经过初等变换后得方阵`\B`，则（）

A. \[\left| {\rm{A}} \right| = \left| {\rm{B}} \right|\]
B. \[\left| A \right| \ne \left| B \right|\]
C. \[\left| A \right|\left| B \right| \ge {\rm{0}}\]
D. 若`\| A| = 0`，则`\| B| = 0`

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设`\A,B`为`\n`阶矩阵，`\| A | = 2,| B | = - 3`，则`\| | 2A^** || B^T|| = ` （）

A. \[3 \cdot {2^{2{n^2} + n}}\]
B. \[ - 3 \cdot {2^{2{n^2} + n}}\]
C. \[3 \cdot {2^{2{n^2} - n}}\]
D. \[ - 3 \cdot {2^{2{n^2} - n}}\]

设\[A = \left( {\begin{array}{*{20}{c}} a&b&b\\ b&a&b\\ b&b&a \end{array}} \right)\]，`\ A`的伴随阵的秩为1，则（）

A. `\a = b`或`\a + 2b = 0`
B. `\a \ne b`且`\a + 2b = 0`
C. `\a = b`或`\a + 2b \ne 0`
D. `\a \ne b`且`\a + 2b \ne 0`

设`\A`是`\m \times n`矩阵，`\B`是`\n \times m`矩阵，则（）

A. `\m > n`时必有`\| AB | = 0`
B. `\m < n`时必有`\| AB | = 0`
C. `\m > n`时必有`\| AB | \ne 0`
D. `\m < n`时必有`\| AB | \ne 0`

设\[A = \left( {\begin{array}{{20}{c}} {{a_{11}}}&{{a_{12}}}&{{a_{13}}}&{{a_{14}}}\\ {{a_{21}}}&{{a_{22}}}&{{a_{23}}}&{{a_{24}}}\\ {{a_{31}}}&{{a_{32}}}&{{a_{33}}}&{{a_{34}}}\\ {{a_{41}}}&{{a_{42}}}&{{a_{43}}}&{{a_{44}}} \end{array}} \right),B = \left( {\begin{array}{{20}{c}} {{a_{14}}}&{{a_{13}}}&{{a_{12}}}&{{a_{11}}}\\ {{a_{24}}}&{{a_{23}}}&{{a_{22}}}&{{a_{21}}}\\ {{a_{34}}}&{{a_{33}}}&{{a_{32}}}&{{a_{31}}}\\ {{a_{44}}}&{{a_{43}}}&{{a_{42}}}&{{a_{41}}} \end{array}} \right)\]，\[{P_1} = \left( {\begin{array}{{20}{c}} 0&0&0&1\\ 0&1&0&0\\ 0&0&1&0\\ 1&0&0&0 \end{array}} \right),{P_2} = \left( {\begin{array}{{20}{c}} 1&0&0&0\\ 0&0&1&0\\ 0&1&0&0\\ 0&0&0&1 \end{array}} \right)\]，若`\A`可逆，则`\B^{ - 1} = `（）

A. \[{A^{ - 1}}{P_1}{P_2}\]
B. \[{P_2}{A^{ - 1}}{P_1}\]
C. \[{P_1}{P_2}{A^{ - 1}}\]
D. \[{P_1}{A^{ - 1}}{P_2}\]