WBJEE · Maths · Matrices
If \(A\) and \(B\) square matrices of the same order and \(A B=3 I\), then \(A^{-1}\) is equal to
- A \(3 \mathrm{~B}\)
- B \(\frac{1}{3} \mathrm{~B}\)
- C \(3 \mathrm{~B}^{-1}\)
- D \(\frac{1}{3} \mathrm{~B}^{-1}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{3} \mathrm{~B}\)
Step-by-step Solution
Detailed explanation
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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