If $A=\left[\begin{array}{ccc}1 & 3 & -2 \ -3 & 0 & -5 \ 2 & 5 & 0\end{array} ight]$ and $A(\operatorname{adj} A)=K I$, then the value of $K$ is (where $I$ is unit matrix of order 3)

Question

If $A=\left[\begin{array}{ccc}1 & 3 & -2 \ -3 & 0 & -5 \ 2 & 5 & 0\end{array}ight]$ and $A(\operatorname{adj} A)=K I$, then the value of $K$ is (where $I$ is unit matrix of order 3)

Aicharya · Accepted Answer

$\because A(\operatorname{adj} A)=|A| . I$ Hence $\mathrm{K}=|\mathrm{A}|=25$

If $A=\left[\begin{array}{ccc}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array}\right]$ and…

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