If A and B are non-singular matrices of order three such that a d j A B = 1 1 1 1 α 1 1 1 α and B 2 a d j A = α 2 + 3 α - 8 , then the value of α is equal to

Step-by-step solution

a d j A B = 1 1 1 1 α 1 1 1 α = 1 α 2 - 1 - 1 α - 1 + 1 1 - α = α 2 - 2 α + 1 = α - 1 2 ⇒ A B 2 = α - 1 2 and B 2 a d j A = B 2 A 2 = A B 2 = α - 1 2 = α 2 + 3 α - 8 ⇒ α 2 - 2 α + 1 = α 2 + 3 α - 8 ⇒ 5 α = 9 ⇒ α = 9 5