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If $A=\left[\begin{array}{ccc}1 & -2 & 2 \\ 2 & -6 & 5 \\ 5 & 0 & 4\end{array}\right]$, then $\operatorname{Adj} A=$
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Verified Answer
The correct answer is:
$\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & -1 \\ 30 & -10 & -2\end{array}\right]$
$$
\begin{aligned}
A & =\left[\begin{array}{ccc}
1 & -2 & 2 \\
2 & -6 & 5 \\
5 & 0 & 4
\end{array}\right] \\
|A| & =1(-24)+2(8-25)+2(0+30) \\
& =-24-34+60=2
\end{aligned}
$$
Cofactor matrix of $A, C=\left[\begin{array}{ccc}-24 & 17 & 30 \\ 8 & -6 & -10 \\ 2 & -1 & -2\end{array}\right]$
$\operatorname{Adj}(A)=C^T=\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & -1 \\ 30 & -10 & -2\end{array}\right]$
\begin{aligned}
A & =\left[\begin{array}{ccc}
1 & -2 & 2 \\
2 & -6 & 5 \\
5 & 0 & 4
\end{array}\right] \\
|A| & =1(-24)+2(8-25)+2(0+30) \\
& =-24-34+60=2
\end{aligned}
$$
Cofactor matrix of $A, C=\left[\begin{array}{ccc}-24 & 17 & 30 \\ 8 & -6 & -10 \\ 2 & -1 & -2\end{array}\right]$
$\operatorname{Adj}(A)=C^T=\left[\begin{array}{ccc}-24 & 8 & 2 \\ 17 & -6 & -1 \\ 30 & -10 & -2\end{array}\right]$
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