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 $\Delta = \begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}$ 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 $\begin{vmatrix} A_1 & B_1 & C_1 \\ A_2 & B_2 & C_2 \\ A_3 & B_3 & C_3 \end{vmatrix}$ is

Sum of minor and co-factor of element $2020$ of $\Delta=\left|\begin{array}{rrr}2019 & 2020 & 2021 \\ 2022 & 2023 & 2024 \\ 2025 & 2026 & 2027\end{array}\right|$ is . . . . . . .

Consider the matrices $A=\begin{bmatrix} x & y & 0 \\ -3 & 1 & 2 \\ 1 & -2 & z \end{bmatrix}$ and $B=\begin{bmatrix} 1 & -2 & -2 \\ 2 & 0 & 1 \\ 2 & 1 & 0 \end{bmatrix}$. If the cofactors of the elements $z$,$1$ (in the $3^{rd}$ row,$2^{nd}$ column),and $x$ of $A$ are $9, 4, 3$ respectively,then $AB=$

Find the minors and cofactors of all the elements of the determinant $\left|\begin{array}{rr}1 & -2 \\ 4 & 3\end{array}\right|$.

The sum of the products of the elements of any row of a determinant $A$ with the corresponding co-factors is always equal to