The sum of the cofactors of the elements of the second row of the matrix $\begin{bmatrix} 1 & 3 & 2 \\ -2 & 0 & 1 \\ 5 & 2 & 1 \end{bmatrix}$ is

Write the minors and cofactors of the elements of the following determinant: $\left|\begin{array}{ccc}1 & 0 & 4 \\ 3 & 5 & -1 \\ 0 & 1 & 2\end{array}\right|$

If $A = [a_{ij}]_{3 \times 3} = \begin{bmatrix} 1 & 3 & 3 \\ -1 & 2 & 2 \\ 1 & 1 & 4 \end{bmatrix}$ and $A_{ij}$ is the cofactor of $a_{ij}$,then the value of $a_{31}A_{31} + a_{32}A_{32} + a_{33}A_{33}$ is equal to

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 . . . . . . .

If $A$ is a $3 \times 3$ matrix and the matrix obtained by replacing the elements of $A$ with their corresponding cofactors is $\begin{bmatrix} 1 & -2 & 1 \\ 4 & -5 & -2 \\ -2 & 4 & 1 \end{bmatrix}$, then a possible value of the determinant of $A$ is

The co-factors of the elements of the second column of $\begin{bmatrix} 1 & -1 & 2 \\ 3 & 2 & 1 \\ -1 & 3 & 4 \end{bmatrix}$ are: