We prove the matchgate identities in a simpler way, by showing the functions of matchgates are in a closed set generated by two growth operations, called juxtaposition and jumper by Matthew Cook. Because of these identities, instead of all exponentially many values, polynomial many values are enough to record a matchgate function. These facts give a #Pl-PM algorithm directly. Using the known matchgate that simulates crossing, this new algorithm can be adapted to both Pfaffian and Determinant.