Voltage buffer with ideal Op-Amp (positive feedback) - Instability
I know that the circuits which employ negative feedback are stable


Any feedback system is potentially unstable. What might seem like negative feedback at low frequencies can easily turn to positive feedback at higher frequencies.


  whereas those which employ positive feedback are not stable.


Also, incorrect. A comparotor that uses hysteresis can be regarded as stable when one or the other threshold has been exceeded.


  How can I prove that a voltage buffer (ideal op-amp) which uses
  positive feedback is not stable?


You can derive a stable condition for an op-amp with positive feedback but, if you introduce the slightest bit of noise as an influence, the circuit becomes a massive noise amplifier. If you then model input offset voltage and bias currents and how those change with temperature you get an unpredictable circuit.