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.

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?