Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If $A$ is a square matrix of order 3 with $|A| \neq 0$, then which one of the following is correct?
MathematicsMatricesNDANDA 2013 (Phase 2)
Options:
  • A $|a d j A|=|A|$
  • B $|a d j A|=|A|^{2}$
  • C $|a d j A|=|A|^{3}$
  • D $|a d j A|^{2}=|A|$
Solution:
1442 Upvotes Verified Answer
The correct answer is: $|a d j A|=|A|^{2}$
$|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{\mathrm{n}-1} \quad$ \{n is order of square matrix $\}$
If A is square matrix of order 3 , then $|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{2}$

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.