1. The problem statement, all variables and given/known data
(i) Verify that 5 is a primitive 4th root of unity in F_13.
(ii) Let F be the 4x4 matrix whose (i, j)th entry is 5ij in F_13 for i, j = 0,1,2, 3.
Compute F(hat) and verify that F(hat)F= I.
2. Relevant equations