Let 2 1 0 1 2 - 1 0 - 1 2 . If a d j ( a d j a d j 2 A ) = ( 16 ) n , then n is equal to

Step-by-step solution

Given that A = 2 1 0 1 2 - 1 0 - 1 2 and a d j a d j a d j 2 A = 16 n . We know that a d j A = A n - 1 and a d j a d j A = A n - 1 2 Similarly, a d j a d j a d j A = A n - 1 3 where n is the order of the square matrix. Let us find A . A = 2 2 × 2 - - 1 - 1 - 1 1 × 2 - 0 - 1 + 0 1 × - 1 - 0 × 2 = 2 3 - 2 + 0 = 4 ⇒ 2 A n - 1 3 = 2 A 3 - 1 3 = 2 A 8 = 2 8 3 A 8 ⇒ 2 24 × 4 8 = 16 n ⇒ 16 6 × 16 4 = 16 n ⇒ 16 10 = 16 n ⇒ n = 10 Therefore, the value of n is 10 .