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September 2nd, 2009, 06:31 PM  #1 
Newbie Joined: Sep 2009 Posts: 6 Thanks: 0  If A and B are symmetric, show A+B is also symmetric
Here's how the problem reads: Let A and B be symmetric matrices. a) Show that A+B is symmetric. b) Show that AB is symmetric if and only if AB=BA. 
September 3rd, 2009, 07:51 AM  #2 
Senior Member Joined: Feb 2009 Posts: 172 Thanks: 5  Re: If A and B are symmetric, show A+B is also symmetric
a) Since , and you have that . That is, is symmetric. b) Suppose that is symmetric. Then you have that . But . Hence, . Suppose . Since and you have that that is, is symmetric. 

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