Question #194045

Prove that if A is a square matrix then AAT and A + A T are symmetric.


1
Expert's answer
2021-05-17T16:19:39-0400



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^T

=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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