A) 0
B) \[{{A}^{2}}+{{B}^{2}}\]
C) \[{{A}^{2}}+2AB+{{B}^{2}}\]
D) \[A+B\]
Correct Answer: B
Solution :
\[{{(A+B)}^{2}}=(A+B).(A+B)={{A}^{2}}+AB+BA+{{B}^{2}}\] ?.1 Since\[B=-{{A}^{-1}}BA\] \[AB=A(-{{A}^{-1}}BA)=-(A{{A}^{-1}})BA[\because A(BC)=(AB)C]\]\[\therefore \]\[AB=-BA\]put in (1), we get \[{{(A+B)}^{2}}={{A}^{2}}-BA+BA+{{B}^{2}}\] \[{{(A+B)}^{2}}={{A}^{2}}+{{B}^{2}}\]You need to login to perform this action.
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