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If the matrix $\mathrm{A}=\left[\begin{array}{rrr}1 & 3 & 1 \\ -1 & 2 & -3 \\ 0 & 1 & 2\end{array}\right]$ then $\operatorname{adj}(\operatorname{adj} A)$ is equal to
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$\left[\begin{array}{llr}12 & 36 & 12 \\ -12 & 24 & -36 \\ 0 & 12 & 24\end{array}\right]$
$A=\left[\begin{array}{ccc}1 & 3 & 1 \\ -1 & 2 & -3 \\ 0 & 1 & 2\end{array}\right]$
$\begin{aligned} \Rightarrow &|\mathrm{A}|=1 .(4+3)-3(-2+0)+1(-1-0) \\ &=7+6-1=12 \\ & \text { So, adj }(\operatorname{adj} \mathrm{A})=|\mathrm{A}|^{\mathrm{n}-2}=\mathrm{A} \\ &=(12)^{3-2} \mathrm{~A}=12 \mathrm{~A} \\ &=12\left[\begin{array}{ccc}1 & 3 & 1 \\ -1 & 2 & -3 \\ 0 & 1 & 2\end{array}\right] \\ &=\left[\begin{array}{ccc}12 & 36 & 12 \\ -12 & 24 & -36 \\ 0 & 12 & 24\end{array}\right] \end{aligned}$
$\begin{aligned} \Rightarrow &|\mathrm{A}|=1 .(4+3)-3(-2+0)+1(-1-0) \\ &=7+6-1=12 \\ & \text { So, adj }(\operatorname{adj} \mathrm{A})=|\mathrm{A}|^{\mathrm{n}-2}=\mathrm{A} \\ &=(12)^{3-2} \mathrm{~A}=12 \mathrm{~A} \\ &=12\left[\begin{array}{ccc}1 & 3 & 1 \\ -1 & 2 & -3 \\ 0 & 1 & 2\end{array}\right] \\ &=\left[\begin{array}{ccc}12 & 36 & 12 \\ -12 & 24 & -36 \\ 0 & 12 & 24\end{array}\right] \end{aligned}$
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