Why an op-amp's gain and bandwidth are locked in an inverse tradeoff — and can't be maximized at the same time from a single stage.
A standard, uncompensated single-pole-dominant op-amp has a fixed specification called the gain-bandwidth product (GBW, or GBWP) — the frequency at which its open-loop gain rolls off to unity (1, or 0 dB). This single number is a genuine constant for a given op-amp model. For that specific part, the product of whatever closed-loopgain you configure it for — set entirely by external feedback resistors — and the resulting closed-loop bandwidth over which that gain stays flat, is approximately equal to that fixed GBW. Configure the circuit for more gain, and the usable bandwidth shrinks to match. Configure it for less gain, and the bandwidth opens back up. It isn't a coincidence and it isn't adjustable independently — it's a direct consequence of how the op-amp's internal compensation shapes its open-loop response.