If A = 1 5 ! 6 ! 7 ! 5 ! 6 ! 7 ! 6 ! 7 ! 8 ! 7 ! 8 ! 9 ! , then adj adj 2 A is equal to

Step-by-step solution

Given, A = 1 5 ! 6 ! 7 ! 5 ! 6 ! 7 ! 6 ! 7 ! 8 ! 7 ! 8 ! 9 ! ⇒ A = 1 5 ! 6 ! 7 ! 5 ! 6 ! 7 ! 6 ! 7 ! 8 ! 7 ! 8 ! 9 ! ⇒ A = 1 5 ! 6 ! 7 ! 5 ! × 6 ! × 7 ! 1 6 42 1 7 56 1 8 72 ⇒ | A | = 2 Now using the property of adjoint of matrix we get, adj adj A = A ( n - 1 ) 2   &   k A = k n A , where n is order of square matrix, Now using the above two formula we get, adj adj 2 A = 2 A 4 = 2 12 A 4 ⇒ adj adj 2 A = 2 12 · 2 4 ⇒ adj adj 2 A = 2 16