Proving Symmetry of AAT: Is it Possible?

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Homework Statement



A matrix S is symmetric if S = ST. Show that AAT is symmetric for any matrix A.

Homework Equations



AAT = (AT)TAT

The Attempt at a Solution



I just said:

A = (AT)T and AT = AT

Therefore AAT is symmetric.

I am unsure if that proves it or if I just went in a circle proving nothing.
 
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If A, B are any matrices, how do you simplify the following expression?

<br /> \left(AB\right)^T<br />

Apply that answer to simplify

<br /> A A^T<br />

and use the hints you provided
 
Ok I think this is right.

(AB)T = BTAT

Then (AAT)T = AAT

Therefore AAT is symmetric because (AT)T = A and AT = AT.
 
I think you have the correct idea. the 'conventional' way of finishing the proof would be to write everything in one string rather than stopping midstream - I have no idea how
picky your professor would be in that regard.
 
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