一般的线性代数教材上,在利用矩阵的初等变换求满秩矩阵A的逆矩阵时。都限于只进行行变换或只进行列变换。本文认为,在这种情况下.行变换和列变换可以混合施行。 由高等代数可知。若A为n阶非奇异(满秩)矩阵,则矩阵A经过有限次初等变换可化为n阶单位矩阵I,也就是说,存在有限个初等矩阵E_1,E_2,…,E_(?),E_((?)-1)….E_(?).使 General linear algebra textbooks, the use of elementary transformation of the matrix to find the inverse of the full rank matrix A. Are limited to only perform line transformation or only column transformation. This paper argues that in this case, line and column transformations can be mixed. It can be seen from advanced algebra. If A is an n-th order non-singular (full rank) matrix, the matrix A can be transformed into an n-th order identity matrix I by a finite number of elementary transformations, that is to say there exist a finite number of elementary matrices E_1, E_2, ..., E _ ((?) - 1) ... .E_ (?)