七、 已知A是n阶实反对称矩阵，即满足A的逆置等于A的相反数 ，试求：当n是奇数时， A的行列式. (5分)
A\u4e3a n\u9636\u53ef\u9006\u77e9\u9635 \u8bf7\u95ee\u5982\u4f55\u8bc1\u660eA\u7684\u884c\u5217\u5f0f\u7684\u9006\u7b49\u4e8eA\u9006\u7684\u884c\u5217\u5f0f\u4f60\u60f3\u8bf4det(A⁻¹) = 1/det(A)\u5427\uff1f\u884c\u5217\u5f0f\u662f\u4e00\u4e2a\u6570\u503c\uff0c\u4e0d\u662f\u77e9\u9635\uff0c\u6ca1\u6709\u9006\u7684\uff0c\u5e94\u8be5\u8981\u8bf4\u5012\u6570\u5173\u7cfb
det(E) = 1
det(A \u00b7 A⁻¹) = 1
det(A) \u00b7 det(A⁻¹) = 1\uff0c\u5b9a\u7406det(AB) = det(A) \u00b7 det(B)
det(A⁻¹) = 1/det(A)\uff0cprovided that det(A) \u2260 0
\u8bc1\u660e: \u7531\u5df2\u77e5, AA' = E
\u6240\u4ee5 |E-A|=|AA'-A|
= |A(A'-E)|
= |A||A'-E|
= 1* |(A-E)'|
= |A-E|
= |-(E-A)|
= (-1)^n|E-A|
= - |E-A|.
\u6545 |E-A| = 0.
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