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If $A$ and $B$ are two matrices such than rank of $A=$ $\mathrm{m}$ and rank of $\mathrm{B}=\mathrm{n}$, then
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Verified Answer
The correct answer is:
$\operatorname{rank}(\mathrm{AB}) \leq \min (\operatorname{rank} \mathrm{A}, \operatorname{rank} \mathrm{B})$
$\because \operatorname{rank}(\mathrm{AB}) \leq \operatorname{rank}(\mathrm{A})$ and $\operatorname{rank}(\mathrm{AB}) \leq \operatorname{rank}(\mathrm{B})$
Therefore $\operatorname{rank}(\mathrm{AB}) \leq \min ($ rank A, rank B)
Therefore $\operatorname{rank}(\mathrm{AB}) \leq \min ($ rank A, rank B)
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