A和B为n阶矩阵,且满足A^2=A,B^2=B,r(A+B-E)=n,证明r(A)=r(B)
人气：116 ℃ 时间：2020-01-31 23:50:21
解答
A^2=A r(E-A)+r(A)=n.
n=r(A+B-E)==r(A)
同理：
n=r(A+B-E)==r(B)
==>r(A)=r(B)
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