Electronic – Capacitor with op-amp

I expect this will oscillate or otherwise not behave as you intend. The TL081 is supposedly unity gain stable, but it is unlikely stable at unity gain and with such a large capacitive load.

Even if the opamp were ideal, your circuit doesn't make sense. A perfect ideal opamp would drive its output to whatever it takes. The cap would just cause lots of current whenever it changes its output voltage.

If your intent is to low pass filter the output, put a resistor in series with the opamp output before the cap. A better answer for a low pass filter using these components is to put the resistor followed by cap to groun on the input of the opamp.

No, there is no way to make an inverting buffer with just an op-amp that does not depend on the resistor values. You can get resistors with very fine accuracy and stability (at an equally impressive price) or you can get networks with matched (in value and in temperature coefficient) where the absolute accuracy may not be so impressive but the ratio is tightly controlled.

There is a way to invert a signal without accurate resistors- the so-called flying capacitor method, but it's fairly complex and resistors are a better solution for most situations down to ppm level accuracy.