A2=[cosθisinθisinθcosθ][cosθisinθisinθcosθ]
=[cos2θ−sin2θ2isinθcosθ2isinθcosθcos2θ−sin2θ]
=[cos2θisin2θisin2θcos2θ]
A3=[cos2θisin2θisin2θcos2θ][cosθisinθisinθcosθ]
=[cos3θisin3θisin3θcos3θ]
Similarly, A5=[cos5θisin5θisin5θcos5θ]=[abcd]
a=cos5θ, b=isin5θ, c=isin5θ
d=cos5θ
a=d,b=c
(1) a2+b2=cos25θ−sin25θ=cos10θ∈(0,1) as θ=24π
(2) a2−d2=0
(3) a2−b2=cos25θ+sin25θ=1
(4) a2−c2=a2−b2=1