Find the inverse of the matrix left[begin{arr | vedclass

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(D) Let $A = \left[\begin{array}{cc}-1 & 5 \ -3 & 2\end{array}ight]$.First,calculate the determinant of $A$:$|A| = (-1)(2) - (5)(-3) = -2 + 15 = 13

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$\frac{1}{13}\left[\begin{array}{cc}2 & -5 \ 3 & -1\end{array}ight]$

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(D) Let $A = \left[\begin{array}{cc}-1 & 5 \ -3 & 2\end{array}ight]$.First,calculate the determinant of $A$:$|A| = (-1)(2) - (5)(-3) = -2 + 15 = 13$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.The adjoint of a $2 	imes 2$ matrix $\left[\begin{array}{cc}a & b \ c & d\end{array}ight]$ is given by $\left[\begin{array}{cc}d & -b \ -c & a\end{array}ight]$.Applying this to matrix $A$:$adj(A) = \left[\begin{array}{cc}2 & -5 \ 3 & -1\end{array}ight]$.The inverse is given by $A^{-1} = \frac{1}{|A|} adj(A)$:$A^{-1} = \frac{1}{13} \left[\begin{array}{cc}2 & -5 \ 3 & -1\end{array}ight]$.

Find the inverse of the matrix $\left[\begin{array}{cc}-1 & 5 \\ -3 & 2\end{array}\right]$ (if it exists).

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