Search any question & find its solution
Question:
Answered & Verified by Expert
If $A=\left[\begin{array}{ll}-2 & 2 \\ -3 & 2\end{array}\right], B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$, then $\left(B^{-1} A^{-1}\right)^{-1}$ is equal to
Options:
Solution:
1341 Upvotes
Verified Answer
The correct answer is:
$\left[\begin{array}{ll}2 & 2 \\ 2 & 3\end{array}\right]$
$\begin{aligned} & A^{-1}=\frac{1}{2}\left[\begin{array}{cc}3 & -2 \\ -2 & 2\end{array}\right], B^{-1}=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right] \\ & B^{-1} A^{-1}=\frac{1}{2}\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]\left[\begin{array}{cc}2 & -2 \\ 3 & -2\end{array}\right] \\ &=\frac{1}{2}\left[\begin{array}{cc}3 & -2 \\ -2 & 2\end{array}\right]=\left[\begin{array}{cc}\frac{3}{2} & -1 \\ -1 & 1\end{array}\right] \\ &\left(B^{-1} A^{-1}\right)^{-1}=2\left[\begin{array}{cc}1 & 1 \\ 1 & \frac{3}{2}\end{array}\right]=\left[\begin{array}{ll}2 & 2 \\ 2 & 3\end{array}\right]\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.