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We demonstrate a polarization-insensitive all-optical flip-flop based on a multimode-interference bistable laser diode. Polarization-insensitive flip-flop operation is demonstrated with the set power as low as -3 dBm, by applying 0.3% tensile strain to the multiple quantum wells gain medium. The output state of polarization is stabilized to the transverse-magnetic mode irrespective of input polarization, indicating that our device also offers a polarization-stabilizing function. Dynamic switching is achieved without waveform distortion even when the input polarization state is scrambled.