Hi,pleasehelp solve this Matrix Question ?

Given N = 1 andM = 4N.M-th root of 1 is given by = j , where exp [-2 j / N], j = (-1)^1/2.

Note j²= 1. It can be verified as :

^M= ^4N= = (j )^4N= j^4N4N= (j⁴)^N4N= 1

Hint:^4N= [exp (-2 j / N)]^4N= exp (-4 j) =cos 4 - j sin 4 = 1

Use M-th root of 1, construct (M x M) square matrix S. With (a,b) element of S is given by :

s_a,b= = ^(a-1)(b-1), a = 1,2,........M ; b =1.2,........M