Create exact inverted signal
This is a kind of silly question, but not in a bad way, it can be used as a teachable moment.

The issue you have isn't so much that resistors can be poorly matched, it is that you're assuming op-amps are ideal. That is, "the only source of error is from the resistors, so if I get rid of those I will reach nirvana".

Even if you get matched resistor made from un-obtainium you'll not achieve your (unstated - or rather unparameterized) goal.

In reality all op-amps have issues with input current balancing, input voltage offsets, frequency dependant behaviour etc.  Your solution must account for all of these.

And the parameters of your solution space will dictate what can be ignored and what can't be corrected. Hint -> this means you need to give more details as to what is needed, BW, etc.

One classical technique is to use a chopper stabilized amplifier which switches back and forth and self corrects for op-amp and in some topologies, even the resistor network non-linearity.

Another technique is to use switched cap techniques.