設A是一个n阶非异方陣,我們可用下法来求A的逆方陣A~(-1),即在A的右方列一个n阶单位方陣E,得到一个n×2n矩陣,对这个矩陣作初等行变換使前n列变为E則后n阶此时即組成A~(-1)。这个方法在許多綫性代数教科书中均可找到。我們不妨称这个方法为“記录矩陣法”。这个方法甚为簡捷。本文中我們来研究这个方法在向量問題及綫性方程組中的一些应用。可以看出,在这些問題之应用中本法仍不失为一个簡捷的計算法。 Let A be an n-order non-hetero-squared matrix. We can use the following method to find A’s inverse square matrix A~(-1), that is, in the right column of A, we have an n-order square matrix E to get an n*2n matrix. The matrix is ​​used for elementary row transformation so that the first n columns are changed to E and then the n-th order is composed of A~(-1). This method can be found in many linear algebra textbooks. We may call this method “record matrix method.” This method is very simple. In this paper, we will study some applications of this method in vector problems and linear equations. It can be seen that this law is still a simple calculation method in the application of these problems.