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NDA 2016 Maths · Mathematics · Determinants · hard

If A is a 3×3 matrix with |A|=-2, then |-A^3| is equal to

Single correct option

If AA is a 3×33\times3 matrix with ∣A∣=−2|A|=-2, then ∣−A3∣|-A^3| is equal to
  1. A. −8-8
  2. B. 1616
  3. C. 88
  4. D. −16-16
Show answer and solution

Answer: (C) 88

∣A3∣=∣A∣3=−8|A^3|=|A|^3=-8. For a 3×33\times3 matrix, ∣−B∣=(−1)3∣B∣=−∣B∣|-B|=(-1)^3|B|=-|B|, so ∣−A3∣=−(−8)=8|-A^3|=-(-8)=8. The traps are forgetting the sign change from the scalar −1-1 (giving −8-8) or using ∣A∣2|A|^2.
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Original question written in the NDA 2016 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