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If A is matrix of order $3 \times 2$ and $\mathrm{B}$ is matrix of order $2 \times 3$, then what is $|\mathrm{kAB}|$ equal to (where $\mathrm{k}$ is any scalar quantity)?
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The correct answer is:
$\mathrm{k}^{3} \mid \mathrm{AB}$
As given of $\mathrm{A}$ and $\mathrm{B}$ are $3 \times 2$ and $2 \times 3$ respectively. $\Rightarrow$ order of $\mathrm{AB}$ is $3 \times 3$ $\Rightarrow|\mathrm{kAB}|=\mathrm{k}^{3} \mid \mathrm{AB}$
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