The aircraft type does not necessarily mean the original prop is still on it. The American Aviation Corp. AA-1 Yankee and AA-1A Trainer came with a two-blade fixed-pitch prop. There may be STCs for prop changes based on intended usage or operating areas, mountains of the American west, for example.
The prop manufacturer's nomenclature (Type and SerNo) will tell you what you want to know. Refer these to the propeller manufacturers or your inspection authority A&P and you will get your answer. Do not necessarily believe the aircraft's seller. Have an A&P you trust do an inspection of the aircraft's records as well as the aircraft condition, itself. An A&P can determine the propeller's characteristics and make recommendations re whether it may meet your specific need. Realize that all two-place trainer light aircraft usually have climb props in their original manufacture.
Fixed pitch props are a trade-off. You have to know how and where you will use the aircraft to match the prop to main intended usage. That is why constant speed controllable pitch props come standard for complex aircraft models.
The AA-1B was the first development of the AA-1 Yankee design by Grumman-American when they offered the Bede production designs made by American Aviation Corp. The Yankee had been replaced by the AA-1A Trainer. The AA-1B of G-A was a revised Trainer with greater takeoff weight. G-A further introduced the improved AA-1C, T-Cat and Lynx in 1978 with other changes, including more standard equipment. The AA-1B could be either a TR-2 or Trainer because the TR-2 was a -dash mod of the AA-1A and the AA-1B, having upmarket interior trim, wheel fairings and more avionics. These could have been added later, hence the records check is needed. In 1975 both versions were offered.