Inversion of n x n matrix A matrix F is given:
$$
F = [e^{i\frac{2\pi kl}{n}}]_{k,l=0}^{n-1}
$$
Find $$ F^{-1} $$
I know Gaussian method for inverting matrices but I suppose it doesn't apply to  matrices with not given exact n value. Could you tell me what are the methods for inverting matrices like this?

HINT:
This is a famous matrix, $1/\sqrt{n}\cdot F$ is unitary. One can check this directly or look at  
http://en.wikipedia.org/wiki/Discrete_Fourier_transform#Orthogonality
