Understanding Negative feedback loop circuit with an Ideal Op-Amp
The op amp generates a voltage equal to the difference of the two inputs. Hence, suppose we start with \$V_{out} = 0V = V_{-} = V_{+}\$. Let's consider two cases.

The input becomes positive, \$V_{+}=0.1V\$ . The output is equal to the difference of the two inputs. Thus, it is equal to \$V_+\$, and we end up with \$V_+ = 0.1V = V_{out} = V_-\$.
The input becomes negative, \$V_{+}=-0.1V\$. Again, the output of the op amp is equal to the difference of the two inputs. Thus, it is equal to \$V_+\$, and  we end up with \$V_+ = -0.1V = V_{out} = V_-\$.