1. The problem statement, all variables and given/known data (i) Verify that 5 is a primitive 4th root of unity in F13. (ii) Let F be the 4x4 matrix whose (i, j)th entry is 5ij in F13 for i, j = 0,1,2, 3. Compute F(hat) and verify that F(hat)F= I. 2. Relevant equations The matrix F(hat) is called the inverse discrete Fourier transform of F. 3. The attempt at a solution I have already solved part (i): Since 52 = 15 = -1 (mod 13) and 54 = (-1)2 = 1 (mod 13), we conclude that 5 is a primitive 4th root of unity in F13. But I do not know how to obtain matrix F for part (ii), but I understand that F(hat) is the inverse matrix of F, so if I can find matrix F then I can easily solve for matrix F(hat). If someone can please help me out I'd really appreciate it.