Let $A = {[{a_{ij}}]_{n \times n}}$ be a square matrix and let ${c_{ij}}$ be cofactor of ${a_{ij}}$ in $A$. If $C = [{c_{ij}}]$ ,then

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

The cofactor of the element $'4'$ in the determinant $\left| {\,\begin{array}{*{20}{c}}1&3&5&1\\2&3&4&2\\8&0&1&1\\0&2&1&1\end{array}\,} \right|$ is

Using Cofactors of elements of second row, evaluate $\Delta=\left|\begin{array}{lll}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{array}\right|$

The minors of $ -4$ and  $ 9$  and the co-factors of  $-4$  and $ 9$ in determinant $\,\left| {\,\begin{array}{*{20}{c}}{ – 1}&{ – 2}&3\\{ – 4}&{ – 5}&{ – 6}\\{ – 7}&8&9\end{array}\,} \right|$ are respectively