Why is the Op Amp Gain-Bandwidth Product Constant?

A recurring conversation I have usually starts with two questions: Why is the op amp gain-bandwidth product constant? And, how can we prove that?

The questions refer to the gain-bandwidth product behavior of an op amp after the cutoff frequency. As I showed in this article, Mastering Electronics Design.com: An Op Amp Gain Bandwidth Product, the gain bandwidth product describes the op amp gain dependency on frequency. The open loop graph is shown in Figure 1.

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