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(A) Let $A = \begin{bmatrix} -1 & 2 \ -3 & 5 \end{bmatrix}$. We write $A = IA$,where $I = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$.$\begin{bmatr

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$\begin{bmatrix} 5 & -2 \ 3 & -1 \end{bmatrix}$

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(A) Let $A = \begin{bmatrix} -1 & 2 \ -3 & 5 \end{bmatrix}$. We write $A = IA$,where $I = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$.$\begin{bmatrix} -1 & 2 \ -3 & 5 \end{bmatrix} = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} A$Apply $R_1 	o -R_1$:$\begin{bmatrix} 1 & -2 \ -3 & 5 \end{bmatrix} = \begin{bmatrix} -1 & 0 \ 0 & 1 \end{bmatrix} A$Apply $R_2 	o R_2 + 3R_1$:$\begin{bmatrix} 1 & -2 \ 0 & -1 \end{bmatrix} = \begin{bmatrix} -1 & 0 \ -3 & 1 \end{bmatrix} A$Apply $R_2 	o -R_2$:$\begin{bmatrix} 1 & -2 \ 0 & 1 \end{bmatrix} = \begin{bmatrix} -1 & 0 \ 3 & -1 \end{bmatrix} A$Apply $R_1 	o R_1 + 2R_2$:$\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 5 & -2 \ 3 & -1 \end{bmatrix} A$Thus,$A^{-1} = \begin{bmatrix} 5 & -2 \ 3 & -1 \end{bmatrix}$.

Using elementary transformations,find the inverse of the following matrix,if it exists: $A = \begin{bmatrix} -1 & 2 \\ -3 & 5 \end{bmatrix}$

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