If ${\Delta _1} = \left| {\begin{array}{*{20}{c}}
  {{b^5}{c^6}\left( {{c^3} – {b^3}} \right)}&{{a^4}{c^6}\left( {{a^3} – {c^3}} \right)}&{{a^4}{b^5}\left( {{b^3} – {a^3}} \right)} \\ 
  {{b^2}{c^3}\left( {{b^6} – {c^6}} \right)}&{a{c^3}\left( {{c^6} – {a^6}} \right)}&{a{b^2}\left( {{a^6} – {b^6}} \right)} \\ 
  {{b^2}{c^3}\left( {{c^3} – {b^3}} \right)}&{a{c^3}\left( {{a^3} – {c^3}} \right)}&{a{b^2}\left( {{b^3} – {a^3}} \right)} 
\end{array}} \right|$ and ${\Delta _2} = \left| {\begin{array}{*{20}{c}}
  a&{{b^2}}&{{c^3}} \\ 
  {{a^4}}&{{b^5}}&{{c^6}} \\ 
  {{a^7}}&{{b^8}}&{{c^9}} 
\end{array}} \right|$ then ${\Delta _1}{\Delta _2}$ is equal to

Write Minors and Cofactors of the elements of following determinants : $\left|\begin{array}{rr}2 & -4 \\ 0 & 3\end{array}\right|$

If $P = \left[ {\begin{array}{*{20}{c}}1&\alpha &3\\1&3&3\\2&4&4\end{array}} \right]$ is the adjoint of  $3×3 $ matrix $A$  and $ |A|=4$  then $\alpha $ is equal to 

$\left| {\,\begin{array}{*{20}{c}}{{{\log }_3}512}&{{{\log }_4}3}\\{{{\log }_3}8}&{{{\log }_4}9}\end{array}\,} \right| \times \left| {\,\begin{array}{*{20}{c}}{{{\log }_2}3}&{{{\log }_8}3}\\{{{\log }_3}4}&{{{\log }_3}4}\end{array}\,} \right|=$

Let ${\Delta _1} = \left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right|$ and ${\Delta _2} = \left| {\,\begin{array}{*{20}{c}}{{\alpha _1}}&{{\beta _1}}&{{\gamma _1}}\\{{\alpha _2}}&{{\beta _2}}&{{\gamma _2}}\\{{\alpha _3}}&{{\beta _3}}&{{\gamma _3}}\end{array}\,} \right|$, then ${\Delta _1} \times {\Delta _2}$ can be expressed as the sum of how many determinants