Minors and Cofactors

If $A=\left[\begin{array}{ccc}1& -1& 2\\ 3& 0& -2\\ 1& 0& 3\end{array}\right]$ verify that  $\mathrm{A}\left(\mathrm{adj} \mathrm{A}\right)=\left(\mathrm{adj} \mathrm{A}\right)A=\left|\begin{array}{c}\mathrm{A}\end{array}\right|\mathrm{I}$

Find the adjoint of the following matrix $A=\left[\begin{array}{cc}2& -3\\ 3& 5\end{array}\right]$

Show with the usual notation that for any matrix, $A={\left[a_{ij}\right]}_{3\times 3}, a_{11}{A}_{11}+a_{12}{A}_{12}+a_{13}{A}_{13}=\left|A\right|$.

The cofactors of first column in the determinant $\left|\begin{array}{cc}5& 20\\ 3& -1\end{array}\right|$ are

In the det. $\left|\mathrm{ }\begin{array}{lll}7& 1& -2\\ 8& 0& -1\\ -3& 2& -4\end{array}\mathrm{ }\right|$ the value of ${\mathrm{C}}_{23}$ is-

Find the minor of the element $6$ in the determinant $\Delta =\left|\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right|$.