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Matrix Algebra - Definite vs. Indefinite

Let A be an nxn symmetric matrix such that det {see attachment}. We know from the matrix algebra that the associated quadratic form {see attachment}, where x = (x1,...xn), is either positive-definite, negative- definite or indefinite.
Now assume the diagonal entries of A are all zero. Explain why q(x) is indefinite.
(Hint: A criterion in terms of the signs of the diagonal minors)