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

Question

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, 3, 4, 6, 5

MARKS App · Accepted Answer

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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