T O P I C R E V I E W 
Manu 
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 1true, 2false, 3true is correct.

3 L A T E S T R E P L I E S (Newest First) 
royhaas 
Posted  03/28/2012 : 12:25:14 quote: Originally posted by Manu
I 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. 
Manu 
Posted  03/28/2012 : 10:08:21 I think B^12 = B^4 is not possible. 
royhaas 
Posted  03/28/2012 : 08:50:50 Why do you think 2 is false? 

