A) \[\left| A \right|=\left| B \right|\]
B) \[\left| A \right|=-\left| B \right|\]
C) \[\left| adj\,A \right|=\left| adj\,B \right|\]
D) A is invertible if and only if B is invertible
Correct Answer: A
Solution :
[a] (Multiplying \[{{R}_{2}}\]by -1) (Multiplying \[{{C}_{2}}\]by -1) (Changing \[{{R}_{1}}\]with\[{{R}_{2}}\]) Hence, \[\left| A \right|=-\left| B \right|,\] obviously when \[\left| A \right|\ne 0,\left| B \right|\ne 0.\] Also, \[\left| adjB \right|={{\left| B \right|}^{2}}={{(-\left| A \right|)}^{2}}={{\left| A \right|}^{2}}.\]You need to login to perform this action.
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