If B is invertible, prove that det(B^-1AB)=det(A)

[From: ] [author: ] [Date: 11-11-06] [Hit: ]

or if its wrong show me the steps to proving this?Thanks in advance!-Dude,here order doesnt matter,because det(X) is a real number.det(B)det(A)det(B-1) = det(B-1)det(A)det(B) are always same but B*-1 *A * B and B * A* B^-1 are not always same.......

i did this but i don't know if it's right:

det(B)det(B-1)det(A)det(B)=det(B)det(A…

det(A)det(B)det(B-1)=det(B)det(A)det(B…

det(A)=det(B)det(A)det(B-1)

I didn't think this is right because the order on the right side is different from the original order on the left side. Can you please let me know if what i did is correct, or if it's wrong show me the steps to proving this?

Thanks in advance!

-

Dude,
here order doesn't matter,because det(X) is a real number.det(B)det(A)det(B-1) = det(B-1)det(A)det(B) are always same but B*-1 *A * B and B * A* B^-1 are not always same.

1

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