How Do You Prove Matrices Like AA^T and A+A^T Are Symmetric?

[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.

 

[Office_Shredder]

Showing A+A^T 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+A^T

 

[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?