question_answer

If in the determinant \[\Delta =\left| \begin{matrix}    {{a}_{1}} & {{b}_{1}} & {{c}_{1}}  \\    {{a}_{2}} & {{b}_{2}} & {{c}_{2}}  \\    {{a}_{3}} & {{b}_{3}} & {{c}_{3}}  \\ \end{matrix} \right|\], \[{{A}_{1}},{{B}_{1}},{{C}_{1}}\] etc. be the co-factors of \[{{a}_{1}},{{b}_{1}},{{c}_{1}}\]etc., then which of the following relations is incorrect

A) \[{{a}_{1}}{{A}_{1}}+{{b}_{1}}{{B}_{1}}+{{c}_{1}}{{C}_{1}}=\Delta \]

B) \[{{a}_{2}}{{A}_{2}}+{{b}_{2}}{{B}_{2}}+{{c}_{2}}{{C}_{2}}=\Delta \]

C) \[{{a}_{3}}{{A}_{3}}+{{b}_{3}}{{B}_{3}}+{{c}_{3}}{{C}_{3}}=\Delta \]

D) \[{{a}_{1}}{{A}_{2}}+{{b}_{1}}{{B}_{2}}+{{c}_{1}}{{C}_{2}}=\Delta \]