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  4. If A-1=(1/11) beginpmatrix-3 4 5 -3 endpmatrix, then A =

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Q. If $A^{-1}=\frac{1}{11}\begin{pmatrix}-3 & 4 \\ 5 & -3\end{pmatrix}$, then $A =$

KEAMKEAM 2020

Solution:

$A=\begin{bmatrix}3 & 4 \\ 5 & 3\end{bmatrix}$
$\Rightarrow A^{-1}=\frac{1}{9-20}\begin{bmatrix}3 & -4 \\ -5 & 3\end{bmatrix}$
$=\frac{1}{-11}\begin{bmatrix}3 & -4 \\ -5 & 3\end{bmatrix}$
$=\frac{1}{11}\begin{bmatrix}-3 & 4 \\ 5 & -3\end{bmatrix}$