设 \( A \)为3阶方阵，已知 \( \left| A \right| = 2 \)，则 \( \left| { { A^{\rm{*}}}} \right|{\rm{ = }} \)______
举一反三
- 设\( A,\;B \) 均为\( n \) 阶方阵，则必有（ ）. A: \( {(A + B)^2} = {A^2} + 2AB + {B^2} \) B: \( \left| {A + B} \right| = \left| A \right| + \left| B \right| \) C: \( \left| {AB} \right| = \left| A \right|{\kern 1pt} \left| B \right| \) D: \( {\left( {AB} \right)^{\rm T}} = {A^{\rm T}}{B^{\rm T}} \)
- 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`
- 设\( \alpha {\rm{ = }}{\left( {1,0,1} \right)^T},\,A = \alpha {\alpha ^T} \)，则\( \left| A \right|{\rm{ = }} \)______
- 设 \( A \)， \( B \)为 \( n \)阶方阵，已知\( A \ne B \) ，则 \( \left| A \right| \ne \left| B \right| \).
- 设\( A \) 为 \( n \)阶方阵，则 \( \left| {5A} \right| = 5\left| A \right| \).