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,$\displaystyle H \in \mathbb{R}^{n \times n} $ with $\displaystyle n \in \{5,6,7\}$

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

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

How can I make this leading to contradiction?

Regards

Re: real hadamard matrices of order 5 do not exist