设A,B都是三阶矩阵,,且满足(A*)-1B=ABA+2A2,则B=_______.

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问题 设A,B都是三阶矩阵,,且满足(A*)-1B=ABA+2A2,则B=_______.

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答案[*]

解析 |A|=-3,A*=|A|A-1=-3A-1,则(A*)-1B=ABA+2A2化为AB=ABA+2A2,注意到A可逆,得B=BA+2A或-B=3BA+6A,则=-6A(E+3A)-1
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