用numpy 测试了下，旋转矩阵的交换律（还是结合律）

import numpy as np

m = np.array([[1,2,3],[4,5,6],[0,0,1]])
n = np.array([[11,22,33],[44,55,66],[0,0,1]])
m_t = np.transpose(m)

begin = np.array([5,13,1])

z = m_t * n *m *begin
print(z)

x1 = m * begin
x2 = n * x1
x3 = m_t * x2
print(x3)