Show that if $H$ is a Hadamard matrix then any matrix obtained by multiplying a row or column of $H$ by $-1$ or by exchanging two rows or two columns of $H$ is still a Hadamard matrix.
Show that if $H$ is a Hadamard matrix then any matrix obtained by multiplying a row or column of $H$ by $-1$ or by exchanging two rows or two columns of $H$ is still a Hadamard matrix.