若\(n\)阶方阵\(A\)经若干次初等变换后变成\(B\),则\(\left| A \right| = \left| B \right|\).
举一反三
- 设\( A \)为\( n \) 阶方阵, \( B \)是\( A \)经过若干次初等变换后得到的矩阵,则( ) A: \( \left| A \right| = \left| B \right| \) B: \( \left| A \right| \ne \left| B \right| \) C: 若\( \left| A \right| = 0 \) ,则必有 \( \left| B \right| = 0 \) D: 若\( \left| A \right| > 0 \),则一定有\( \left| B \right| > 0 \)
- 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\( n \) 阶方阵 \( A,B \)相似,则 \( \left| A \right| = \left| B \right| \).
- 设\( A \) 为 \( n \)阶方阵,则 \( \left| {5A} \right| = 5\left| A \right| \).
- 设\( A,B \)均为\( n \)阶方阵,则必有( ) A: \( \left| {A + B} \right| = \left| A \right| + \left| B \right| \) B: \( AB = BA \) C: \( \left| {AB} \right| = \left| {BA} \right| \) D: \( {\left( {A + B} \right)^{ - 1}} = {A^{ - 1}} + {B^{ - 1}} \)