A) \[A=-B\]
B) \[A=B\]
C) \[B=0\]
D) \[B={{A}^{2}}\]
Correct Answer: B
Solution :
Let \[[A]=\left[ \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right]\]and \[[B]=\left[ \begin{matrix} {{c}_{1}} & {{c}_{2}} & {{c}_{3}} \\ {{a}_{1}} & {{a}_{2}} & {{a}_{3}} \\ {{b}_{1}} & {{b}_{2}} & {{b}_{3}} \\ \end{matrix} \right]=\left[ \begin{matrix} {{a}_{1}} & {{a}_{2}} & {{a}_{3}} \\ {{b}_{1}} & {{b}_{2}} & {{b}_{3}} \\ {{c}_{1}} & {{c}_{2}} & {{c}_{3}} \\ \end{matrix} \right]\] \[={{[A]}^{t}}\] As we know, det \[(A)=det\,(A')\] \[\therefore \] \[A=B\]
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