A) \[{{A}^{2}}{{B}^{2}}\]
B) \[{{A}^{2}}\]
C) \[{{B}^{2}}\]
D) I
Correct Answer: C
Solution :
[c]: \[(A+B)(A-B)={{A}^{2}}-{{B}^{2}}\] \[\Rightarrow \]\[AA+BA-AB-BB={{A}^{2}}-{{B}^{2}}\] \[\Rightarrow \]\[{{A}^{2}}+BA-AB-{{B}^{2}}={{A}^{2}}-{{B}^{2}}\] \[\Rightarrow \]\[BA-AB=0\Rightarrow BA=AB\] \[\therefore \]\[{{(AB{{A}^{-1}})}^{2}}={{(BA{{A}^{-1}})}^{2}}={{(BI)}^{2}}={{B}^{2}}\]You need to login to perform this action.
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