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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Matrices

NDA 2023 · Mathematics · Matrices

If A, B and C are square matrices of order 3 and (BC)=2 ( A) , then...

If A,BandA, B andCaresquarematricesoforder3andare square matrices of order 3 and\operatorname\det(\mathrm{BC})=2 \operatorname\det(\mathrm{ A}),thenwhatisthevalueof, then what is the value of\operatorname\det (2A−1BC)?\left(2 \mathrm{ A}^{-1} \mathrm{BC}\right)?

Options

  1. A16
  2. B8
  3. C4
  4. D2

Correct answer

A. 16

Step-by-step solution

Given ∣BC∣=2∣A∣|B C|=2|A| Now, ∣2 A−1BC∣=23∣ A−1∣∣BC∣=8×1∣ A∣×2∣ A∣=16\left|2 \mathrm{~A}^{-1} \mathrm{BC}\right|=2^3\left|\mathrm{~A}^{-1}\right||\mathrm{BC}|=8 \times \frac{1}{|\mathrm{~A}|} \times 2|\mathrm{~A}|=16
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