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NDA 2018 Maths · Mathematics · Matrices · hard

If A is a 3×3 matrix with |A|=3, what is the value of |adj(2A)|?

Single correct option

If AA is a 3×33\times3 matrix with ∣A∣=3|A|=3, what is the value of ∣adj⁡(2A)∣|\operatorname{adj}(2A)|?
  1. A. 576
  2. B. 144
  3. C. 72
  4. D. 24
Show answer and solution

Answer: (A) 576

∣2A∣=23⋅3=24|2A|=2^3\cdot3=24. For a 3×33\times3 matrix ∣adj⁡B∣=∣B∣2|\operatorname{adj}B|=|B|^{2}, so the answer is 242=57624^2=576. The distractors apply the adjoint rule or the scalar rule only partially.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake