After so many years of using linear algebra, until today I finally understand the meaning of matrix multiplication.  matrix*vector is linear combination of the columns of the matrix, and vector*matrix is linear combination of the row of the matrix. Then from this standpoint, the meaning of permutation matrix becomes so obvious. Thank you Prof. Strang.####[['Prof. Strang', 'Instructor', 'POS'], ['matrix multiplication', 'Mathematical_Related_Concept', 'POS'], ['linear algebra', 'Mathematical_Related_Concept', 'POS']]