Is this matrix full-rank?

From: mb (mentalrubberbands_at_hotmail.com)
Date: 07/20/04 

Date: 20 Jul 2004 01:35:18 -0700

I suspect that the following proposition is true:
A symmetric matrix with zeros at the diagonal is full-rank.
How do you prove that? Or is the proposition false?

I would appreciate any kind of help. Thank you.

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