A) \[{{(14)}^{4}}\]
B) \[{{(14)}^{3}}\]
C) \[{{(14)}^{2}}\]
D) \[{{(14)}^{1}}\]
Correct Answer: A
Solution :
[a] We know that adj (adj A)\[=|A{{|}^{n-2}}A,\,\,if|A|\ne 0\], provided order of A is n. \[\therefore \] \[adj\text{ }\left( adj\text{ }A \right)=\left| A \right|A\left( as\,\,n=3 \right)\] \[\therefore \] \[det\text{ }\left( adj\text{ }\left( adj\text{ }A \right) \right)={{\left| \text{ }A\text{ } \right|}^{3}}\text{ }det\text{ }A={{\left| \text{ }A\text{ } \right|}^{4}}\] \[But\left| A \right|=\left[ \begin{matrix} 1 & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1 \\ \end{matrix} \right]=14\] \[\therefore \] det \[(adj\,\,(adj\,\,A))={{(14)}^{4}}\]
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