Let $A \in \mathcal{M}_{n}(\{-1,1\})$. Show that the following statements are equivalent: (a) $n^{2} \in S(A)$. (b) There exist $X$ and $Y$ in $\{-1,1\}^{n}$ such that $A = X\,{}^{t}Y$. (c) $A$ is a rank 1 matrix.
Let $A \in \mathcal{M}_{n}(\{-1,1\})$. Show that the following statements are equivalent:
(a) $n^{2} \in S(A)$.
(b) There exist $X$ and $Y$ in $\{-1,1\}^{n}$ such that $A = X\,{}^{t}Y$.
(c) $A$ is a rank 1 matrix.