## real hadamard matrices of order 5 do not exist

Hi there

I've got to show that there do not exist real Hadamard matrices of order 5,6 or 7.

So assume H is a Hadamard Matrix, $H \in \mathbb{R}^{n \times n}$ with $n \in \{5,6,7\}$

Then we have $H*H^T=n*I_n$ where $I_n$ denotes the identity Matrix in $\mathbb{R}^{n \times n}$

Furthermore $H*H^T*H*H^T=n^2*I_n$ ???