Q68 / 180 · KCET 2016 · Mathematics

If \( A \) is any square matrix of order \( 3 \times 3 \) then \( |3 A| \) is equal to

  • A
    \( 3|\mathrm{~A}| \)
  • B
    \( \frac{1}{3} \mid A \)
  • Correct answer
    C
    \( 27|\mathrm{~A}| \)
  • D
    \( 9 \mathrm{~A} \mid \)

Solution

We know that, \( |K \mathrm{~A}|=K^{n}|\mathrm{~A}| \) So, \( |3 \mathrm{~A}|=3^{3}|7 \mathrm{~A}| \) \( =27|\mathrm{~A}| \)

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

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