Search any question & find its solution
Question:
Answered & Verified by Expert
If A is semy square matrix of order 3 and det $\mathrm{A}=5$, then what is $\operatorname{det}\left[(2 \mathrm{~A})^{-1}\right]$ equal to?
Options:
Solution:
2198 Upvotes
Verified Answer
The correct answer is:
$1 / 40$
$|A|=5 \Rightarrow|2 A|=2^{3} \times 5=40$
$\Rightarrow\left|A^{-1}\right|=\frac{1}{|A|} \Rightarrow\left|(2 A)^{-1}\right|=\frac{1}{|2 A|}=\frac{1}{40}$
$\Rightarrow\left|A^{-1}\right|=\frac{1}{|A|} \Rightarrow\left|(2 A)^{-1}\right|=\frac{1}{|2 A|}=\frac{1}{40}$
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.