Finding hermitian conjugate and inverse of a complex matrix

Question

I have the following matrix: $$ F = [e^{i\frac{2\pi kl}{n}}]^{n-1}_{k,l=0} \in \mathbb{C}^{n,n} $$ for $n = 1,2,3,...,i$

I need to find $F^HF$ and $F^{-1}$ where $F^H$ is a hermitian conjugate matrix. I don't know exactly where to start, so it would be great if you could point me in the right direction.

Answer 1

The hermitian of a matrix $A$ satisfies $(A^H)_{k,l}= A_{l,k}^*$, where by $*$ here I mean conjugate. You can use this formulate to easily find the hermitian of $F$, right? And what happens when you multiply $F^H$ times $F$?