If $A = \begin{bmatrix} 1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$ 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

Write the minors and cofactors of the elements of the following determinant: $\left|\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right|$

Let $A = \begin{bmatrix} 3 & 1 & 2 \\ 1 & 2 & 0 \\ 1 & 1 & 4 \end{bmatrix}$ and $pC_{11} + 4C_{21} - 5C_{32} = -2$, where $C_{ij}$ denotes the cofactor of an element $a_{ij}$ of matrix $A$. Find the value of $p$.

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 $A = \begin{bmatrix} 1 & 0 & 2 \\ 2 & 1 & 3 \\ 0 & 3 & -5 \end{bmatrix}$,where $A_{ij}$ is the cofactor of the element $a_{ij}$ of matrix $A$,then $a_{21} A_{21} + a_{22} A_{22} + a_{23} A_{23} = $

Using cofactors of elements of the third column,evaluate $\Delta = \left| \begin{array}{ccc} 1 & x & yz \\ 1 & y & zx \\ 1 & z & xy \end{array} \right|$.