Abstract: The concepts of row (column) transposed matrix and row (column) symmetric matrix are given, and problems like the determinant, characteristic, reversibility, similarity and symmetry are also examined. The results show: N-order matrix, together with its transposed matrix of rows and columns, all of the three have the same reversibility; the transposed matrix of rows and the transposed matrix of columns have much in common in similarity, and some other relevant results are obtained.