Stupid question

do you know if any of your components in your system invert phase?

Typically Red is HOT in an electrical circuit. In audio, Red is considered Hot and the Red from the amp should be connected to the red for the speaker, UNLESS your amp, or Pre-amp Inverts the Phase, then you want to connect the red to black and black to red to correct the inversion of phase from the upstream component.

It doesn't matter, so long as you connect positive on the amp to positive on the speaker and negative on the amp to negative on the speaker. Kind of like jumping a car battery, but less dangerous if you mess it up.

If you do mess them up, it can sound bad. I have no idea why. Since the signal is AC, it's negative voltage some of the time and positive voltage some of the time, so it shouldn't make any difference. But I have heard them connected wrong and for some reason it does sound terrible.

Out of phase speakers do matter...it's all about "suck in or suck out" and if out of phase they "suck in" and that sucks.

Since the signal contains positive and negative values, the speaker is SUPPPOSED to suck in some of the time and push out the other part anyway. Speakers don't just move from neutral/zero to some positive distance from the voice coil. They also move backwards just as much. That's my understanding anyway, based on the fact that the signal doesn't favor plus or minus (otherwise it would be a combination of DC and AC).
Picture a bass note of 40 Hz with no overtones. A pure, repeating cosine wave. While it's above 0 volts, it's pushing the speaker. While it's below it's pulling. If you were to switch polarity, all you'd be doing is inverting the waveform. So it's still pushing and pulling. The only difference is you start off in the opposite direction. So for 1/80th of a second at the beginning it would be different. And somehow this makes an audible difference!
There must be more to it...