Q47 / 160 · AP EAMCET 2021 (25 Aug Shift 2) · Mathematics

If each element, of a determinant of third order with value $A$, is multiplied by 3 , then the value of newly formed determinant is

  • A
    3A
  • B
    9A
  • Correct answer
    C
    27A
  • D
    -27A

Solution

Since, we know that, if $P$ is any matrix of order n. Then, $|K P|=K^n|P|$, where $K$ is constant. Given $|P|=A$, where $P$ is of order 3 . $$ \therefore \quad|3 P|=3^3|P|=27 A $$

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

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