If $A=\left[\begin{array}{ccc}1 & 2 & 3 \ -1 & 1 & 2 \ 1 & 2 & 4\end{array} ight]$, and $A(\operatorname{adj} A)=k I$, then the value of $(k+1)^4$ is

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If $A=\left[\begin{array}{ccc}1 & 2 & 3 \ -1 & 1 & 2 \ 1 & 2 & 4\end{array}ight]$, and $A(\operatorname{adj} A)=k I$, then the value of $(k+1)^4$ is

Aicharya · Accepted Answer

$|A|=\left|\begin{array}{ccc} 1 & 2 & 3 \ -1 & 1 & 2 \ 1 & 2 & 4 \end{array}ight|=1(0)-2(-6)+3(-3)=3$ We know that $\mathrm{A}(\operatorname{adj} \mathrm{A})=|\mathrm{A}| \mathrm{I}$ $\begin{aligned} & 	herefore \mathrm{A}(\operatorname{adj} \mathrm{A})=3 \mathrm{I} \Rightarrow \mathrm{k}=3 \ & (\mathrm{k}+1)^4=(3+1)^4=256 \end{aligned}$

If $A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$, and…

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