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Question: Answered & Verified by Expert
Let $A$ and $B$ be matrices of order $3 \times 3$. If $A B=0$, then which of the following can be concluded?
MathematicsMatricesNDANDA 2010 (Phase 2)
Options:
  • A $A=0$ and $B=0$
  • B $|A|=0$ and $|B|=0$
  • C Either $|A|=0$ or $|B|=0$
  • D Either $A=0$ or $B=0$
Solution:
2887 Upvotes Verified Answer
The correct answer is: Either $A=0$ or $B=0$
If AB = 0 , then it may be concluded that either $\mathrm{A}=0$ or $\mathrm{B}=0$
But, it should be noticed that it is not necessary that either $\mathrm{A}=0$ or $\mathrm{B}=0$.

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