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Question: Answered & Verified by Expert
If $A$ and $B$ square matrices of the same order and $A B=3 I$, then $A^{-1}$ is equal to
MathematicsMatricesWBJEEWBJEE 2009
Options:
  • A $3 \mathrm{~B}$
  • B $\frac{1}{3} \mathrm{~B}$
  • C $3 \mathrm{~B}^{-1}$
  • D $\frac{1}{3} \mathrm{~B}^{-1}$
Solution:
1493 Upvotes Verified Answer
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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