2005 Putnam A4

Let $H$ be an $n \times n$ matrix all of whose entries are $\pm 1$ and

whose rows are mutually orthogonal. Suppose $H$ has an $a \times b$ submatrix

whose entries are all $1$. Show that $ab \leq n$.

设 $H$ 为 $n \times n$ 矩阵，其所有条目均为 $\pm 1$ 且

其行相互正交。假设 $H$ 有一个 $a \times b$ 子矩阵

其参赛作品均为 1 美元。显示 $ab \leq n$。