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If $A$ and $B$ square matrices of the same order and $A B=3 I$, then $A^{-1}$ is equal to
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The correct answer is:
$\frac{1}{3} \mathrm{~B}$
Hints: $\mathrm{AB}=3 \mathrm{I}, \mathrm{A}^{-1} \cdot \mathrm{AB}=3 \cdot \mathrm{A}^{-1} \mathrm{I} \Rightarrow \mathrm{B}=3 \mathrm{~A}^{-1} \Rightarrow A^{-1}=\frac{1}{3} \mathrm{~B}$
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