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

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

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

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

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

Write the minors and cofactors of the elements of the following determinant: $\left|\begin{array}{ll}a & c \\ b & d\end{array}\right|$