Furthermore by some skills of algebra, it is proved that the set of all pythagorean number matrixes is a finitely generated group, and a set of generators of the finitely generated group is given.

• 利用相关代数技巧，证明由所有的勾股矩阵构成的集合T是一个关于矩阵乘法的有限生成群。同时，给出该有限生成群的一个生成元组。