If A = 1 - 1 1 2 1 - 3 1 1 1 , 10 B = 4 2 2 - 5 0 α 1 - 2 3 and B = A - 1 then the value of α is

Step-by-step solution

Given, A = 1 - 1 1 2 1 - 3 1 1 1 Then, A = 1 1 + 3 + 1 2 + 3 + 1 2 - 1 ⇒ A = 10 Also, C 11 = 4 ,   C 12 = - 5 ,   C 13 = 1 ,   C 21 = 2 ,   C 22 = 0 ,   C 23 = - 2 ,   C 31 = 2 ,   C 32 = 5 ,   C 33 = 3 And Adj ( A ) = C 11 C 21 C 31 C 12 C 22 C 32 C 13 C 23 C 33 = 4 2 2 - 5 0 5 1 - 2 3 We know that, A - 1 = 1 A · Adj A ⇒ A - 1 = 1 10 4 2 2 - 5 0 5 1 - 2 3 Also given that, B = A - 1 and 10 B = 4 2 2 - 5 0 α 1 - 2 3 ⇒ 4 2 2 - 5 0 α 1 - 2 3 = 4