# Help on showing matrices are symmetric

1. May 2, 2007

### FlyingDonkey

I'm having trouble understanding a certain matrix problem.

-Show that AA^T and A^TA are symmetric.
-Show that A+A^T is symmetric.

Any help would be greatly appreciated.

Last edited: May 2, 2007
2. May 2, 2007

### Office_Shredder

Staff Emeritus
Showing A+AT is symmetric should be trivial... write out A as an nxn matrix (it needs to be square for addition to be defined!) with entries $$a_{i,j}$$, and you should be able to calculate directly the i,jth entry of A+AT

3. May 2, 2007

### Dick

Symmetric means A^T=A. And you know that (A+B)^T=A^T+B^T and (AB)^T=(B^T)(A^T), yes?

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