In this paper we synthesize a family of hexagonal arrays, SA(r), that implement matrix multiplication. We have observed that the execution time of hexagonal array, that has minimal number of processing elements for a given problem size, can be reduced if the number of PEs is increased. Since the execution time and the number of PEs are two most important performance measures of the systolic array, we take their product AT^2 , AT^2 = Ω_{r}(n)T^2_{exe}, to compare the arrays from this family. With respect to this performance measure the best array is obtained for r = [n/2], where n is a dimension of square matrices while r indicates the extension, in terms of rows, of the array that has minimal number of processing elements for a given problem size.