If A= [ cc 2 & 2 -3 & 2 ], B= [ cc 0 & -1 1 & 0 ] then (B^ -1 A^ … - Vidyadip

MCQ

If $A=\left[\begin{array}{cc}2 & 2 \\ -3 & 2\end{array}\right], B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$ then $\left(B^{-1} A^{-1}\right)^{-1}=$

✓
$\left[\begin{array}{cc}2 & -2 \\ 2 & 3\end{array}\right]$
B
$\left[\begin{array}{cc}2 & 2 \\ -2 & 3\end{array}\right]$
C
$\left[\begin{array}{cc}2 & -3 \\ 2 & 2\end{array}\right]$
D
$\left[\begin{array}{cc}1 & -1 \\ -2 & 3\end{array}\right]$

✓

Answer

Correct option: A.

$\left[\begin{array}{cc}2 & -2 \\ 2 & 3\end{array}\right]$

(a) : $A=\left[\begin{array}{cc}2 & 2 \\ -3 & 2\end{array}\right], B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$
$|A|=4+6=10 \neq 0$ and $|B|=0+1=1 \neq 0$
$\therefore \quad A^{-1}, B^{-1}$ exists
So, $\left(B^{-1} A^{-1}\right)^{-1}=\left(A^{-1}\right)^{-1}\left(B^{-1}\right)^{-1}=A B$
$=\left[\begin{array}{cc}2 & 2 \\ -3 & 2\end{array}\right]\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]=\left[\begin{array}{cc}0+2 & -2+0 \\ 0+2 & 3+0\end{array}\right]=\left[\begin{array}{cc}2 & -2 \\ 2 & 3\end{array}\right]$

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