If \[\Delta =\left| \,\begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix}\, \right|\] and \[{{A}_{1}},{{B}_{1}},{{C}_{1}}\]denote the co-factors of \[{{a}_{1}},{{b}_{1}},{{c}_{1}}\] respectively, then the value of the determinant \[\left| \begin{matrix} {{A}_{1}} & {{B}_{1}} & {{C}_{1}} \\ {{A}_{2}} & {{B}_{2}} & {{C}_{2}} \\ {{A}_{3}} & {{B}_{3}} & {{C}_{3}} \\ \end{matrix} \right|\] is [MP PET 1989]

If \[\Delta =\left| \,\begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}

1.	If \[\Delta =\left\| \,\begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix}\, \right\|\] and \[{{A}_{1}},{{B}_{1}},{{C}_{1}}\]denote the co-factors of \[{{a}_{1}},{{b}_{1}},{{c}_{1}}\] respectively, then the value of the determinant \[\left\| \begin{matrix} {{A}_{1}} & {{B}_{1}} & {{C}_{1}} \\ {{A}_{2}} & {{B}_{2}} & {{C}_{2}} \\ {{A}_{3}} & {{B}_{3}} & {{C}_{3}} \\ \end{matrix} \right\|\] is [MP PET 1989]
A.	\[\Delta \]
B.	\[{{\Delta }^{2}}\]
C.	\[{{\Delta }^{3}}\]
D.	0
Answer» C. \[{{\Delta }^{3}}\]

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