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Question: Answered & Verified by Expert
If A is a matrix of order $\mathrm{p} \times \mathrm{q}$ and $\mathrm{B}$ is a matrix of order $\mathrm{s} \times \mathrm{t}$, under which one of the following conditions does AB exist?
MathematicsMatricesNDANDA 2006 (Phase 2)
Options:
  • A $\mathrm{p}=\mathrm{t}$
  • B $\mathrm{p}=\mathrm{s}$
  • C $q=t$
  • D $\mathrm{q}=\mathrm{s}$
Solution:
1528 Upvotes Verified Answer
The correct answer is: $\mathrm{q}=\mathrm{s}$
If A is a matrix of order $\mathrm{p} \times \mathrm{q}$ and $\mathrm{B}$ is a matrix of order s $\times \mathrm{t}$, then $\mathrm{AB}$ will exist when the number of column in $\mathrm{A}$ is equal to the number of rows in $\mathrm{B}$ $\Rightarrow \mathrm{q}=\mathrm{s}$

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