A non-volatile Hf_0.5Zr_0.5O₂(HZO)-based Metal-Ferroelectric-Metal (MFM) inverter enabling AND/XNOR operations for Computation-in-Memory CiM) is proposed. Owing to the symmetric threshold voltage V_th) shift in the nFET and pFET of the MFM inverter, a digitized output after the multiply operation is successfully demonstrated for the first time with non-volatile memory, enabling the high precision CiM. In addition, the MFM inverter has the advantage of a large memory window (MW) because a large partial programming voltage is structurally applied to the MFM capacitor. Moreover, the MW and the endurance were intensively studied to clarify the key factors for reliable operation. Together with the process compatible FeRAM as a working memory, the MFM inverter has the potential to achieve low-power, high-density, and high precision non-volatile CiM systems.