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 and $\mathrm{B}$ be two matrices such that $\mathrm{AB}$ is defined. If $\mathrm{AB}=0$, then which one of the following can be definitely concluded?
MathematicsMatricesNDANDA 2006 (Phase 1)
Options:
  • A $\mathrm{A}=0$ or $\mathrm{B}=0$
  • B $\mathrm{A}=0$ and $\mathrm{B}=0$
  • C A and B are non-zero square matrices
  • D A and B cannot both be non-singular
Solution:
2835 Upvotes Verified Answer
The correct answer is: A and B are non-zero square matrices
Since, $\mathrm{AB}$ is defined, neither A nor $\mathrm{B}$ is singular i.e., they are non-zero matrix and if $\mathrm{AB}=0$ both $\mathrm{A}$ and $\mathrm{B}$ are square matrix. So, Aand B are non-zerosquare matrices.

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.