[math] \newcommand{\mathds}{\mathbb}[/math]

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In the context of the previous exercise, prove that the cases

[[math]] 3+2+2\quad,\quad 7 [[/math]]

do not interact, in the sense that a regular [math]7\times7[/math] Hadamard matrix has either all scalar products between the rows of type [math]3+2+2[/math], or of type [math]7[/math].