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If $\left(\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right) A=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$, then the matrix $a$ is
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Verified Answer
The correct answer is:
$\left(\begin{array}{cc}2 & -1 \\ -3 & 2\end{array}\right)$
We have,
$\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
Let
$B=\left[\begin{array}{ll}
2 & 1 \\
3 & 2
\end{array}\right]$
$\therefore \quad B A=I$
$A=B^{-1} I$
$A=B^{-1}$
$\therefore \quad B^{-1}=\left[\begin{array}{cc}2 & -1 \\ -3 & 2\end{array}\right]$
Hence, $A=\left[\begin{array}{cc}2 & -1 \\ -3 & 2\end{array}\right]$
$\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
Let
$B=\left[\begin{array}{ll}
2 & 1 \\
3 & 2
\end{array}\right]$
$\therefore \quad B A=I$
$A=B^{-1} I$
$A=B^{-1}$
$\therefore \quad B^{-1}=\left[\begin{array}{cc}2 & -1 \\ -3 & 2\end{array}\right]$
Hence, $A=\left[\begin{array}{cc}2 & -1 \\ -3 & 2\end{array}\right]$
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