Prove that if A is a square matrix then AAT and A + A T are symmetric.
Let A be any matrix.
Also let B=AAT
Now BT=(AAT)T=(AT)TAT=AATB^T =(AA^T )^T =(A^T )^T A^T =AA^TBT=(AAT)T=(AT)TAT=AAT
=B
[ Since (AT)T=A]
So AAT
is a symmetric matrix.
Let B=A+AT
Now, BT=AT+A [ Since (AT)T=A]
or, BT=B.
So B is symmetric matrix.
And B= A+AT
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