题目内容

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`

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

已知方阵`\A`满足`\A^3 - 5A + 6E = O`，则`\A^{ - 1} = ` （）

A. \[\frac{1}{6}(5E - {A^2})\]
B. \[\frac{1}{6}(5E + {A^2})\]
C. \[\frac{1}{6}(5E - A)\]
D. \[\frac{1}{6}(5E + A)\]

设`\A`为3阶非零矩阵,当`\A^T = A^**`，则`\R(A) = ` （）

A. 1
B. 2
C. 3
D. 由已知无法确定