Assume \(a\) and \(b\) are both real numbers. Determine which of these statements must necessarily be true:

A) If \(a>b\), then \(a^2>b^2\)

B) If \(|a|>b\), then \(a^2>b^2\)

C) If \(a>|b|\), then \(a^2>b^2\)

D) If \(a^2>b^2\), then \(a>b\)

E) If \(a\neq|b|\), then \(a^2\neq b^2\)

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