A) \[162\]
B) \[{{(162)}^{2}}\]
C) \[256\]
D) \[{{(256)}^{2}}\]
Correct Answer: B
Solution :
\[{{A}^{2}}-4A+4I=O\Rightarrow {{(A-2I)}^{2}}=O\Rightarrow A=2I\] \[B=A({{A}^{4}}+4{{A}^{3}}+6{{A}^{2}}+4A+I)=A{{(A+I)}^{4}}\] \[=2I\,{{(3I)}^{4}}=162\,I\] \[\therefore \det .(B)={{(162)}^{2}}\]You need to login to perform this action.
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