53. Let A be a symmetric idempotent matrix. Prove that $$-frac{1}{2} le a_{ij} le frac{1}{2}$$ for all

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53. Let A be a symmetric idempotent matrix. Prove that

$$-\frac{1}{2} \le a_{ij} \le \frac{1}{2}$$ for all i ≠ j.

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