Let A = 1 0 0 0 α β 0 β α and | 2 A | 3 = 2 21 where α , β ∈ Z , Then a value of α is

Step-by-step solution

Given: A = 1 0 0 0 α β 0 β α and 2 A 3 = 2 21 Now, 2 A 3 = 2 21 ⇒ 2 A = 2 7 ⇒ 2 3 A = 2 7 ⇒ A = 16 ⇒ α 2 - β 2 = 16 Now, taking value from the option we get, α = 5 as α , β ∈ Z , so for other value of α , β is not a integer.