Find the minor of element $6$ in the determinant $\Delta=\left|\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right|$

If $\Delta = \left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right|$ and ${A_1},{B_1},{C_1}$denote the co-factors of ${a_1},{b_1},{c_1}$ respectively, then the value of the determinant $\left| {\begin{array}{*{20}{c}}{{A_1}}&{{B_1}}&{{C_1}}\\{{A_2}}&{{B_2}}&{{C_2}}\\{{A_3}}&{{B_3}}&{{C_3}}\end{array}} \right|$ is

Find adjoint of each of the matrices $\left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 3 & 5 \\ -2 & 0 & 1\end{array}\right]$

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 

If $\left| {\begin{array}{*{20}{c}}
1&1&1\\
a&b&c\\
{{a^2}}&{{b^2}}&{{c^2}}
\end{array}} \right| = 5$ , then $\left| {\begin{array}{*{20}{c}}
{b{c^2} – {b^2}c}&{{a^2}c – a{c^2}}&{a{b^2} – b{a^2}}\\
{{b^2} – {c^2}}&{{c^2} – {a^2}}&{{a^2} – {b^2}}\\
{c – b}&{a – c}&{b – a}
\end{array}} \right|$ is equal to