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Question: Answered & Verified by Expert
If the matrix $\mathrm{AB}$ is a zero matrix, then which one of the following is correct?
MathematicsMatricesNDANDA 2012 (Phase 2)
Options:
  • A A must be equal to zero matrix or B must be equal to zeromatrix.
  • B A must be equal to zero matrix and $\mathrm{B}$ must be equal to zeromatrix.
  • C It is not necessary that either $\mathrm{A}$ is zero matrix or $\mathrm{B}$ is zeromatrix.
  • D None of the above
Solution:
1507 Upvotes Verified Answer
The correct answer is: It is not necessary that either $\mathrm{A}$ is zero matrix or $\mathrm{B}$ is zeromatrix.
If matrix $\mathrm{AB}=0$ then it is not necessary that either A is zero matrix or $\mathrm{B}$ is zero matrix.

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