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 . . . . . . .

For determinant $A = \begin{vmatrix} 1 & 2 & 13 \\ 3 & 0 & 5 \\ 6 & 7 & 11 \end{vmatrix}$,if $p, q, r$ are co-factors of elements $13, 5$ and $11$ respectively,then $p + 3q + 6r = $ . . . . . . .

If the cofactors of the elements $3$,$7$ and $6$ of the matrix $\begin{bmatrix} 1 & 2 & 3 \\ 4 & -1 & 7 \\ 2 & 4 & 6 \end{bmatrix}$ are $a$,$b$ and $c$ respectively,then $\begin{bmatrix} a & b & c \end{bmatrix} \begin{bmatrix} 1 \\ 4 \\ 2 \end{bmatrix} + \begin{bmatrix} a & b & c \end{bmatrix} \begin{bmatrix} 3 \\ 7 \\ 6 \end{bmatrix} = $

If in the determinant $\Delta = \begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}$,$A_1, B_1, C_1$ etc. are the co-factors of $a_1, b_1, c_1$ etc.,then which of the following relations is incorrect?

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:

If $A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6 \end{bmatrix}$ and $A_{ij}$ are the cofactors of $a_{ij}$,then $a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13}$ is equal to