Show that if $H$ is a Hadamard matrix of order $n$ then there exists a Hadamard matrix of order $n$ whose coefficients of the first row are all equal to 1. Deduce that if $n \geq 2$ then $n$ is even.
Show that if $H$ is a Hadamard matrix of order $n$ then there exists a Hadamard matrix of order $n$ whose coefficients of the first row are all equal to 1. Deduce that if $n \geq 2$ then $n$ is even.