Inverting or Differential Amplifier? (Or neither?)
You're correct; this will output 100 mV as drawn.  The reason for this is the amplifier outputs whatever voltage is required to set its inputs equal.  Since one input is fixed at 100 mV, the other one must be driven to 100 mV.  This happens when the output is at 100 mV.  Since every node in the circuit is at 100 mV, no current will flow through the resistors (well, ignoring any current flowing in to the op amp input pins).