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Question: Answered & Verified by Expert
Let $A$ and $B$ be two square matrices of order 3 and $A B=O_{3}$, where $O_{3}$ denotes the null matrix of order 3. Then,
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Options:
  • A must be $A=O_{3}, B=O_{3}$
  • B if $A \neq O_{3}$, must be $B \neq O$,
  • C if $A=O_{3}$. must be $B \neq O_{3}$
  • D may be $A \neq O_{3} . B \neq O_{3}$
Solution:
1193 Upvotes Verified Answer
The correct answer is: may be $A \neq O_{3} . B \neq O_{3}$
Since, product of two non-null matrix can be a null matrix.
Therefore, may be
$$
A \neq O_{3}, B \neq O_{3}
$$

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