Let B = 1 3 α 1 2 3 α α 4 , α > 2 be the adjoint of a matrix A and A = 2 . Then α - 2 α α B α - 2 α α is equal to

Step-by-step solution

We have been given that B = 1 3 α 1 2 3 α α 4 , α > 2 And adj ( A ) = B , | A | = 2 ⇒ | adj ( A ) | = | B | We know that a d j A = A n - 1 ⇒ 2 2 = ( 8 - 3 α ) - 3 ( 4 - 3 α ) + α ( - α ) ⇒ α 2 - 6 α + 8 = 0 ⇒ ( α - 4 ) ( α - 2 ) = 0 α = 4 , 2 but α > 2 so α = 4 Now   α - 2 α α B α - 2 α α =   4 - 8 4 1 3 4 1 2 3 4 4 4 4 - 8 4 = 12 12 8 4 - 8 4 = 48 - 96 + 32 = - 16 Hence