If [ ll 2 & 1 7 & 4 ] A [ cc -3 & 2 5 & -3 ]= [ ll 1 & 0 0 & 1 ],… - Vidyadip

MCQ

If $\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right] A \left[\begin{array}{cc}-3 & 2 \\ 5 & -3\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, then matrix A equals

✓
$\left[\begin{array}{cc}7 & 5 \\ -11 & -8\end{array}\right]$
B
$\left[\begin{array}{ll}2 & 1 \\ 5 & 3\end{array}\right]$
C
$\left[\begin{array}{cc}7 & 1 \\ 34 & 5\end{array}\right]$
D
$\left[\begin{array}{cc}5 & 3 \\ 13 & 8\end{array}\right]$

✓

Answer

Correct option: A.

$\left[\begin{array}{cc}7 & 5 \\ -11 & -8\end{array}\right]$

(A) If $XAY = I$, then $A = X ^{-1} Y ^{-1}=( YX )^{-1}$
Here, $YX =\left[\begin{array}{cc}-3 & 2 \\ 5 & -3\end{array}\right]\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right]$
$=\left[\begin{array}{cc}8 & 5 \\ -11 & -7\end{array}\right]$
$\therefore \quad A=\left[\begin{array}{cc}8 & 5 \\ -11 & -7\end{array}\right]^{-1}$
$=\left[\begin{array}{cc}7 & 5 \\ -11 & -8\end{array}\right]$

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