Question

If A = [(cosθ,i sinθ),(i sinθ, cosθ)], (θ = π/24) and A⁵ = [(a,b),(c,d)], where i = √-1, then which one of the following is not true? 

(1) 0 ≤ a² + b² ≤ 1 

(2) a² – d² = 0 

(3) a² – b² = 1/2 

(4) a² – c² = 1

Answer 1

(3) a² – b² = 1/2 

(4) a² - c² = cos² 5θ + sin² 5θ = 1