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Top quark pair production and top quark properties at CDF

We present the most recent measurements of top quark pairs production and top quark properties in proton-antiproton collisions with center-of-mass energy of 1.96 TeV using CDF II detector at the Tevatron. The combination of top pair production cross section measurements and the direct measurement of top quark width are reported. The test of Standard Model predictions for top quark decaying into $b$-quarks, performed by measuring the ratio $R$ between the top quark branching fraction to $b$-quark and the branching fraction to any type of down quark is shown. The extraction of the CKM matrix element $|V_{tb}|$ from the ratio $R$ is discussed. We also present the latest measurements on the forward-backward asymmetry ($A_{FB}$) in top anti-top quark production. With the full CDF Run II data set, the measurements are performed in top anti-top decaying to final states that contain one or two charged leptons (electrons or muons). In addition, we combine the results of the leptonic forward-backward asymmetry in $t\bar t$ system between the two final states. All the results show deviations from the next-to-leading order (NLO) standard model (SM) calculation.