A) \[A\]
B) \[{{A}^{-1}}\]
C) \[-A\]
D) \[-{{A}^{-1}}\]
Correct Answer: B
Solution :
Given, \[B={{A}^{6}}-{{A}^{5}},\] where \[{{A}^{3}}=A+I\] \[\Rightarrow \] \[B={{({{A}^{3}})}^{2}}-{{A}^{3}}{{A}^{2}}\] \[={{(A+I)}^{2}}-(A+I){{A}^{2}}\] \[={{A}^{2}}+{{I}^{2}}+2AI-{{A}^{3}}-{{A}^{2}}I\] \[=I+2A-(A+I)\] \[\Rightarrow \] \[B=A\] \[\therefore \] Inverse of \[B={{A}^{-1}}\]You need to login to perform this action.
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