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
linear algebra
2009-02-20 7:00 pm
回答 (1)
2009-02-20 7:23 pm
✔ 最佳答案
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.
參考: Physics king
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