Q154 / 270 · NDA 2016 (Phase 2) · Mathematics

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

  • A
    $1 / 10$
  • B
    $2 / 5$
  • C
    $8 / 5$
  • Correct answer
    D
    $1 / 40$

Solution

$\begin{aligned} & |A|=5 \Rightarrow|2 A|=2^3 \times 5=40 \\ & \Rightarrow\left|A^{-1}\right|=\frac{1}{|A|} \Rightarrow\left|(2 A)^{-1}\right|=\frac{1}{|2 A|}=\frac{1}{40}\end{aligned}$

Hence, the correct answer is option: 'D'.

Relevant Questions