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Manu
Average Member

Australia
9 Posts

 Posted - 03/27/2012 :  10:03:11 For each of the following statements, select whether the statement is true or false for all n × n invertible matrices A, B , C. (Note that you are being asked whether the statement is true or false for all n × n invertible matrices A, B, C, not just for some invertible A, B, C.)1. (ABA^-1)^8 = A^8B^8A^-8 2. B^12 = B^4 ⇒ B^-1 = B^7 3. A^-1 = BC ⇒ C^-1 = AB Is the answer 1-true, 2-false, 3-true is correct.

royhaas
Moderator

USA
3059 Posts

 Posted - 03/28/2012 :  08:50:50 Why do you think 2 is false?

Manu
Average Member

Australia
9 Posts

 Posted - 03/28/2012 :  10:08:21 I think B^12 = B^4 is not possible.

royhaas
Moderator

USA
3059 Posts

 Posted - 03/28/2012 :  12:25:14 quote:Originally posted by ManuI think B^12 = B^4 is not possible.It is true if B=I. Also, consider the 2X2 complex matrix diag[(1+i)/2]. It's easy to show that B^8=I. There are other examples.
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