The sum of the minor and the cofactor of the element $7$ in the determinant $\left|\begin{array}{ccc}2 & 3 & 5 \\ 1 & 0 & 7 \\ -1 & -2 & 4\end{array}\right|$ is . . . . . .

If $\Delta = \begin{vmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{vmatrix}$ and $A_{ij}$ is the cofactor of $a_{ij}$,then the value of $\Delta$ is given by:

Let $A = [a_{ij}] = \begin{bmatrix} \log_5 128 & \log_4 5 \\ \log_5 8 & \log_4 25 \end{bmatrix}$. If $A_{ij}$ is the cofactor of $a_{ij}$,$C_{ij} = \sum_{k=1}^2 a_{ik} A_{jk}$,$1 \leq i, j \leq 2$,and $C = [C_{ij}]$,then $8|C|$ is equal to:

If the value of a third order determinant is $16$,then the value of the determinant formed by replacing each of its elements by its cofactor is

If $A = [a_{ij}]_{3 \times 3} = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7 \end{bmatrix}$ and $A_{ij}$ is the cofactor of $a_{ij}$,then $a_{11} A_{21} + a_{12} A_{22} + a_{13} A_{23}$ is equal to

If $A = [a_{ij}]_{3 \times 3} = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 4 & 1 \\ 2 & 6 & 3 \end{bmatrix}$ and $A_{ij}$ is the cofactor of $a_{ij}$,then the value of $a_{21} A_{21} + a_{22} A_{22} + a_{23} A_{23}$ is equal to: