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
Let A be a square matrix of order $\mathrm{n} \times \mathrm{n}$ where $\mathrm{n} \geq 2 .$ Let $\mathrm{B}$ be a matrix obtained from A with first and second rows interchanged. Then which one of the following is correct?
MathematicsMatricesNDANDA 2007 (Phase 1)
Options:
  • A $\operatorname{det} \mathrm{A}=\operatorname{det} \mathrm{B}$
  • B $\operatorname{det} \mathrm{A}=-\operatorname{det} \mathrm{B}$
  • C $\mathrm{A}=\mathrm{B}$
  • D $A=-B$
Solution:
2259 Upvotes Verified Answer
The correct answer is: $\operatorname{det} \mathrm{A}=-\operatorname{det} \mathrm{B}$
A be a square matrix of order $\mathrm{n} \times \mathrm{n}$ where $\mathrm{n} \geq 2 . \mathrm{B}$ be a matrix obtained from A with first and second rows interchanged. Then, det $A=-$ det $B$. Since interchanging any two rows makes the sign change with same value.

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.