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If A is an invertible square matrix of the order n such that A ≠ 1 and a d j a d j A = A 2 n 2 - 7 n + 7 , then the sum of all possible values of n is

Options

  1. A3
  2. B4
  3. C6
  4. D5

Correct answer

D. 5

Step-by-step solution

We know that a d j a d j A = A n - 1 2 ⇒ A n - 1 2 = A 2 n 2 - 7 n + 7 ⇒ n 2 - 2 n + 1 = 2 n 2 - 7 n + 7 ⇒ n 2 - 5 n + 6 = 0 Hence, the sum of all values of n is equal to 5

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