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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Matrices

NDA 2019 · Mathematics · Matrices

Paragraph: Let A and B be (3 × 3) matrices with A=4 and B=3 ....

Paragraph:Let AA and BB be (3×3)(3 \times 3) matrices with det⁡⁡A=4\operatorname\det A=4 and det⁡⁡B=3\operatorname\det B=3.
Question:What is det⁡⁡(3AB−1)equalto?\operatorname\det \left(3 \mathrm{AB}^{-1}\right) equal to ?

Options

  1. A12
  2. B18
  3. C36
  4. D48

Correct answer

C. 36

Step-by-step solution

det⁡⁡(3AB−1)=(3)3∣A∣∣B−1∣=27∣A∣∣B∣=27×43=36\operatorname\det\left(3 \mathrm{AB}^{-1}\right)=(3)^3|\mathrm{ A}|\left|\mathrm{B}^{-1}\right|=27 \frac{|A|}{|B|}=27 \times \frac{4}{3}=36
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