If $\mathrm{A}=\left[\begin{array}{cc}2 & 3 \ 5 & -2\end{array} ight]$ and $\mathrm{A}^{-1}=\mathrm{KA}$, then $\mathrm{K}$ is

Question

If $\mathrm{A}=\left[\begin{array}{cc}2 & 3 \ 5 & -2\end{array}ight]$ and $\mathrm{A}^{-1}=\mathrm{KA}$, then $\mathrm{K}$ is

Aicharya · Accepted Answer

$\begin{aligned} & A=\left[\begin{array}{cc}2 & 3 \ 5 & -2\end{array}ight] \ & |A|-4-15=-19 	ext { and adj } A=\left[\begin{array}{cc}-2 & -3 \ -5 & 2\end{array}ight] \ & 	herefore A^{-1}=\frac{-1}{19}\left[\begin{array}{cc}-2 & -3 \ -5 & 2\end{array}ight]=\frac{1}{19}\left[\begin{array}{cc}2 & 3 \ 5 & -2\end{array}ight] \Rightarrow \mathrm{k}=\frac{1}{19}\end{aligned}$

If $\mathrm{A}=\left[\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right]$ and $\mathrm{A}^{-1}=\mathrm{KA}$,…

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