Question

Find adjoint of matrix :
$\left|\begin{array}{ccc}1& -1& 2\\ 2& 3& 5\\ -2& 0& 1\end{array}\right|$

Answer 1

$M_{11}=3$ $M_{12}$ $M_{13}=6$ $M_{21}=-1$ $M_{22}=5$ $M_{23}-2$ $M_{31}=-11$ $M_{32}=1$ $M_{33}=5$ $C_{11}=3$ $C_{12}=-12$ $C_{13}=6$ $C_{21}=1$ $C_{22}=5$ $C_{23}=2$ $C_{31}=-11$ $C_{32}=-1$ $C_{33}=5$
co factor matrix $\left[\begin{array}{ccc}3& -12& 6\\ 1& 5& 2\\ -11& -1& 5\end{array}\right]$
Adj A = Transpose of co-factor matrix
$\left[\begin{array}{ccc}3& -12& 6\\ 1& 5& 2\\ -11& -1& 5\end{array}\right]$
Adj A$=\left[\begin{array}{ccc}3& 1& -11\\ -12& 5& -1\\ 6& 2& 5\end{array}\right]$