In the determinant $\left| \begin{array}{ccc} 0 & 1 & -2 \\ -1 & 0 & 3 \\ 2 & -3 & 0 \end{array} \right|$,the ratio of the cofactor to its minor of the element $-3$ 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

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?

Find the minors and cofactors of the elements of the determinant $\left|\begin{array}{ccc}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{array}\right|$ and verify that $a_{11} A_{31}+a_{12} A_{32}+a_{13} A_{33}=0$.

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

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