E矩阵交换2行或2列后的逆矩阵是本身吗 哪位能帮我讲解一下，单位矩阵仅作行或列交换后，逆矩阵仍然是它...
\u4e00\u9053\u7ebf\u6027\u4ee3\u6570\u9898\uff0c\u8bf7\u95ee\uff0c\u5355\u4f4d\u77e9\u9635\u5bf9\u8c03\u4e24\u884c\u6216\u8005\u4e24\u5217\u540e\uff0cEi,j\u7684\u9006\u77e9\u9635\u4e3a\u4ec0\u4e48\u8fd8\u662f\u5b83\u672c\u8eab\uff1f\u8fd9\u4e2a\u53ef\u4ee5\u8bf4\u660e\u5355\u4f4d\u77e9\u9635
\u8c03\u6362\u4e24\u884ci,j\u540e\u53d8\u6210\u884c
\u521d\u7b49\u53d8\u6362
\u77e9\u9635\u554a\uff0c\u8fd9\u4e2a\u77e9\u9635\u5de6\u4e58\u5230\u4efb\u4f55\u77e9\u9635\u4e0a\u90fd\u76f8\u5f53\u4e8e\u4ea4\u6362\u90a3\u4e2a\u77e9\u9635\u7684\u5bf9\u5e94\u884c
\u6240\u4ee5E(i,j)E(i,j)\u76f8\u5f53\u4e8e\u628aE(i,j)\u4ea4\u6362\u56de\u53bb\u6210\u5355\u4f4d\u77e9\u9635\uff0c\u6240\u4ee5
E(i,j)E(i,j)
=E\uff0c\u6240\u4ee5\u5c31\u662f
\u9006\u77e9\u9635
\u4e3a\u81ea\u8eab
概念混淆了——初等变换前后的矩阵是等价的，即矩阵的秩不变；而矩阵的行列式的值是不一定相等的：如：交换2行（列）值变负，倍加值不变，一行（列）都×k则行列式的值×k等
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