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If $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$ and $X$ is a $2 \times 2$ matrix such that $A X=1$, then $X=$
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The correct answer is:
$\left[\begin{array}{cc}-2 & 1 \\ \frac{3}{2} & -\frac{1}{2}\end{array}\right]$
$\begin{aligned} A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right] & \text { and } A X=I \\ \therefore X=A^{-1} \Rightarrow A^{-1} &=\frac{1}{4-6}\left[\begin{array}{cc}4 & -2 \\ -3 & 1\end{array}\right] \\ &=\frac{1}{-2}\left[\begin{array}{cc}4 & -2 \\ -3 & 1\end{array}\right]=\left[\begin{array}{cc}-2 & 1 \\ \frac{3}{2} & \frac{-1}{2}\end{array}\right] \end{aligned}$
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