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Posted - 03/27/2012 :  09:57:11  Show Profile  Reply with Quote
For each of the following statements, select whether the statement is true or false for all n n matrices A, B , C. (Note that you are being asked whether the statement is true or false for all n n matrices A, B, C, not just for some A, B, C.)

1. (2 A - 8 B)(2 A + 8 B) = 4 A^2 - 64 B^2

2. A(2 I - 8 BA) = (2 I - 8 AB)A

3. A ≠ 0 and AB = A ⇒ B = I

4. (-2 I + AA^T)^ T = -2 I + AA^T

I think the answer is 1-true, 2-false, 3-true, 4-false.
Is it correct or wrong.
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Posted - 03/27/2012 :  10:09:00  Show Profile  Reply with Quote
1. This appears to require commutativity.
2. Check associativity.
3. What if A doesn't have an inverse?
4. Be careful with transpositions.
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