Let α=π/5  and  A=cosαsinα−sinαcosα . If B=A+A2+A3+A4 , then

|A|=1    ∴A is non – singularA2=cos2αsin2α−sin2αcos2α.....A4=cos4αsin4α−sin4αcos4α∵|A|=|A2|=|A3|=|A4|=1If α=π5∑cosα=0 ,∑sinα=sin(α+4α2)sin(4α2)sinα2⇒|B|≠0∴ B is skew symmentric matrix