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Let $A$ and $B$ be $(3 \times 3)$ matrices with $\operatorname{det} A=4$ and det $B=3$.
What is det $\left(3 \mathrm{AB}^{-1}\right)$ equal to ?
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What is det $\left(3 \mathrm{AB}^{-1}\right)$ equal to ?
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The correct answer is:
36
$\operatorname{det}\left(3 \mathrm{AB}^{-1}\right)=(3)^{3}|\mathrm{~A}|\left|\mathrm{B}^{-1}\right|$
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