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NDA 2017 Maths · Mathematics · Matrices · medium

If A is a 3×3 non-singular matrix with |A|=2, then |3A^-1| equals

Single correct option

If AA is a 3×33\times3 non-singular matrix with ∣A∣=2|A|=2, then ∣3A−1∣|3A^{-1}| equals
  1. A. 32\dfrac32
  2. B. 92\dfrac{9}{2}
  3. C. 272\dfrac{27}{2}
  4. D. 5454
Show answer and solution

Answer: (C) 272\dfrac{27}{2}

∣A−1∣=1∣A∣=12|A^{-1}|=\frac1{|A|}=\frac12. Scalar multiplication by 3 of a 3×33\times3 matrix multiplies the determinant by 33=273^3=27. So ∣3A−1∣=272|3A^{-1}|=\frac{27}2. Option 32\frac32 uses a factor 3 instead of 333^3.
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Original question written in the NDA 2017 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