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標題:
linear algebra
發問:
If A and B are n × n matrices and A^?1 exists, show that (ABA^?1)^3 = AB^3A^?1. please provide procedure..or else I can't understand..thank you so much
最佳解答:
其他解答:
linear algebra
發問:
If A and B are n × n matrices and A^?1 exists, show that (ABA^?1)^3 = AB^3A^?1. please provide procedure..or else I can't understand..thank you so much
最佳解答:
此文章來自奇摩知識+如有不便請留言告知
This is easy, please look at the following proof. As A^-1 exists, so A is invertible and AA^-1 = A^-1A = I, the identity matrix of n × n. Now, L.H.S. = (ABA^-1)^3 = (ABA^-1)(ABA^-1)(ABA^-1) = AB(A^-1A)B(A^-1A)BA^-1 = (AB)I(B)IBA^-1 = ABBBA^-1 = AB^3A^-1 = R.H.S. The proof is finished.其他解答:
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