两个（反）对称矩阵的乘积不一定是（反）对称矩阵。举两个反例 证明 两个（反）对称矩阵的乘积不一定是（反）对称矩阵.举两个反例 ...
\u4e24\u4e2a\uff08\u53cd\uff09\u5bf9\u79f0\u77e9\u9635\u7684\u4e58\u79ef\u4e0d\u4e00\u5b9a\u662f\uff08\u53cd\uff09\u5bf9\u79f0\u77e9\u9635.\u4e3e\u4e24\u4e2a\u53cd\u4f8b \u8bc1\u660e
\u7b49\u5f0f\u5de6\u8fb9\u4e24\u4e2a\u77e9\u9635\u662f\u5bf9\u79f0\u7684,\u4e58\u79ef\u4e0d\u5bf9\u79f0.
\u7b49\u5f0f\u5de6\u8fb9\u4e24\u4e2a\u77e9\u9635\u662f\u53cd\u5bf9\u79f0\u7684,\u4e58\u79ef\u4e0d\u662f\u53cd\u5bf9\u79f0. \u8fd9\u7b97\u4e0d\u7b97\u4e24\u4e2a\u4f8b\u5b50\u554a,\u8fd8\u662f\u5404\u8981\u4e24\u4e2a?\u90a3\u5c31\u628a1\u6539\u62102\u4ec0\u4e48\u7684\u628a= =
\u8fd9\u4e2a\u5f88\u597d\u4e3e\u554a.
\uff081\uff09\u5982\u679cA\u3001B\u662f\u5bf9\u79f0\u77e9\u9635\u5219\u53ea\u80fd\u63a8\u51faA=A' ,B=B',\u5219\uff08AB\uff09'=B'A'=BA,BA\u4e0d\u4e00\u5b9a\u7b49\u4e8eAB,\u4e3e\u4f8b\uff1aA=1 2\uff1b2 1 B=-1 2\uff1b1 2
\uff082\uff09\u5982\u679cA\u3001B\u662f\u53cd\u5bf9\u79f0\u77e9\u9635\u5219\u53ea\u80fd\u63a8\u51faA=-A',B=-B',\u5219\uff08AB\uff09'=B'A'=BA,BA\u4e0d\u4e00\u5b9a\u7b49\u4e8e-AB,\u4e3e\u4f8b\uff1aA=0 1 2\uff1b-1 0 1\uff1b-2 -1 0 B=0 2 1\uff1b-2 0 1\uff1b-1 -1 0.
（1）如果A、B是对称矩阵则只能推出A=A' ，B=B'，则（AB）'=B'A'=BA，BA不一定等于AB，举例：A=1 2；2 1 B=-1 2；1 2
（2）如果A、B是反对称矩阵则只能推出A=-A'，B=-B'，则（AB）'=B'A'=BA，BA不一定等于-AB，举例：A=0 1 2；-1 0 1；-2 -1 0 B=0 2 1；-2 0 1；-1 -1 0。
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