Search any question & find its solution
Question:
Answered & Verified by Expert
If $A=\left[\begin{array}{lll}1 & 2 & 1 \\ 3 & 1 & 3\end{array}\right]$ and $B=\left[\begin{array}{ll}2 & 3 \\ 1 & 2 \\ 1 & 2\end{array}\right]$, then $(A B)^{-1}=$
Options:
Solution:
2237 Upvotes
Verified Answer
The correct answer is:
$\left[\begin{array}{cc}\frac{-17}{5} & \frac{9}{5} \\ 2 & -1\end{array}\right]$
$\begin{aligned} & A B=\left[\begin{array}{ll}2+1+1 & 3+4+2 \\ 6+1+3 & 9+2+6\end{array}\right] \\ & =\left[\begin{array}{cc}5 & 9 \\ 10 & 17\end{array}\right] \\ & (A B)-1=\frac{1}{-5}\left[\begin{array}{cc}17 & -9 \\ -10 & 5\end{array}\right]=\left[\begin{array}{cc}-\frac{17}{5} & \frac{9}{5} \\ 2 & -1\end{array}\right]\end{aligned}$
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.