Posted - 03/27/2012 : 09:57:11 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.

1 L A T E S T R E P L I E S (Newest First)

royhaas

Posted - 03/27/2012 : 10:09:00 1. This appears to require commutativity. 2. Check associativity. 3. What if A doesn't have an inverse? 4. Be careful with transpositions.