| 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 1-true, 2-false, 3-true is correct.
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| 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? |
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