若\( A,B \)为同阶方阵，且满足\( AB = O \)，则有（ ）
A: \( A = O \)或\( B = O \)
B: \( \left| A \right| = 0 \)或\( \left| B \right| = 0 \)
C: \( {\left( {A + B} \right)^2} = {A^2} + {B^2} \)
D: \( A \)与\( B \)均可逆
A: \( A = O \)或\( B = O \)
B: \( \left| A \right| = 0 \)或\( \left| B \right| = 0 \)
C: \( {\left( {A + B} \right)^2} = {A^2} + {B^2} \)
D: \( A \)与\( B \)均可逆
举一反三
- 设\( A \) ，\( B \)为\( n \)阶方阵，满足关系 \( AB = O \)，则必有（ ） A: \( A = B = O \) B: \( A + B = O \) C: \( \left| A \right| = 0 \)或\( \left| B \right| = 0 \) D: \( \left| A \right| + \left| B \right| = 0 \)
- 设 \( A,B \)均为 \( n \)阶方阵，则 \( A = O \)的充要条件是（ ） A: \( {A^2} = O \) B: \( \left| A \right| = 0 \) C: \( B \ne O \)且\( AB = O \) D: \( \left| B \right| \ne 0 \)且\( AB = O \)
- 设\( n \)阶方阵\( A,B \) 满足\( A\left( {B - E} \right) = O \)，则必有（ ） A: \( A = O \)且\( B = E \) B: \( A + B = E \) C: 当\( \left| A \right| = 0 \) 时， \( B = E \) D: \( \left| A \right| = 0 \)或\( \left| {B - E} \right| = 0 \)
- 设\( A,B \)为\( n \)阶方阵，且\( AB{\rm{ = }}O \) ，则必有（ ） A: \( BA{\rm{ = }}O \) B: \( A{\rm{ = }}O \)或\( B{\rm{ = }}O \) C: \( A,{\kern 1pt} {\kern 1pt} \,B \)的秩均小于 \( n \) D: \( \left| A \right| = 0 \)或\( \left| B \right| = 0 \)
- 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: \( {\left( {AB} \right)^{\rm T}} = {A^{\rm T}}{B^{\rm T}} \)