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Let \mathrm{A\: \&\: B} be two \mathrm{3\times 3} matrices such that  \mathrm{A B=I \text { and }|A|=\frac{1}{8}} . Then  \mathrm{|\operatorname{adj}(B\: \operatorname{adj}(2 A))|} is equal to

Option: 1

16


Option: 2

32


Option: 3

64


Option: 4

128


Answers (1)

best_answer

\mathrm{|A B|=1 \Rightarrow|A||B|=1 \Rightarrow|B|=8 } \\

\mathrm{|adj(B \: adj(2 A))| =|B\: adj(2 A)|^{2} }\\

                                \mathrm{=|B|^{2} | adj(2A)|^{2}}

                                \mathrm{=|B|^{2}\left(|2 A|^{2}\right)^{2}=|B|^{2}\left(\left(2^{3}|A|\right)^{2}\right)^{2} }\\

                                \mathrm{=8 \times 8 \times\left(8 \times \frac{1}{8}\right)^{4}} \\

                                \mathrm{=64}

Hence the correct answer is option 3.

Posted by

Gautam harsolia

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