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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Matrices

NDA 2016 · Mathematics · Matrices

If A is semy square matrix of order 3 and A=5 , then what is [(2...

If AA is semy square matrix of order 3 and det⁡⁡A=5\operatorname\det A=5, then what is det⁡⁡[(2A)−1]equalto?\operatorname\det \left[(2 \mathrm{ A})^{-1}\right] equal to?

Options

  1. A1/101 / 10
  2. B2/52 / 5
  3. C8/58 / 5
  4. D1/401 / 40

Correct answer

D. 1/401 / 40

Step-by-step solution

∣A∣=5⇒∣2A∣=23×5=40⇒∣A−1∣=1∣A∣⇒∣(2A)−1∣=1∣2A∣=140\begin{aligned} & |A|=5 \Rightarrow|2 A|=2^3 \times 5=40 \\ & \Rightarrow\left|A^{-1}\right|=\frac{1}{|A|} \Rightarrow\left|(2 A)^{-1}\right|=\frac{1}{|2 A|}=\frac{1}{40}\end{aligned}
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