Show that the determinant |a^2+b^2+c^2b ...

Show that the determinant `|a^2+b^2+c^2b c+c a+a bb c+c a+a bb c+c a+a b a^2+b^c+c^2b c+c a+a bb c+c a+a bb c+c a+a b a^2+b^2+c^2|` is always non-negative. When is the determinant zero?

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