摘要
本文首先利用两矩阵的乘法及其相等的定义和克莱姆法则，对ＡＢ＝ＢＡ＝Ｅ＝ＡＢ＝Ｅ（或ＢＡ＝Ｅ）进行了证明。其次将逆矩阵的定义ＡＢ＝ＢＡ＝Ｅ简化为ＡＢ＝Ｅ（或ＢＡ＝Ｅ）后，又证明了逆矩阵存在的必要充分条件及唯一性。
By using Cramer's rule and definition of matrix mtiltiplication and matrix equality,this paper proves the equivalence of AB = BA=E and AB=E(or BA =E).After the deflnition of inverse matrix is modified to AB=E(or BA=E),the paper proves the necessary and sufficient co ndition of invers e matrix's existence.
关键词
复方阵
转置矩阵
克莱姆法则
逆矩阵
矩阵
Complex square matrix,transpose matrix,matrix mtiltiplication and matrix equality,Grammer's rule,inverse matrix,determinant
