# Showing a Matrix is Symmetric

1. Oct 25, 2008

### KillerZ

1. The problem statement, all variables and given/known data

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

2. Relevant equations

AAT = (AT)TAT

3. 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.

2. Oct 25, 2008

If $$A, B$$ are any matrices, how do you simplify the following expression?

$$\left(AB\right)^T$$

$$A A^T$$

and use the hints you provided

3. Oct 25, 2008

### KillerZ

Ok I think this is right.

(AB)T = BTAT

Then (AAT)T = AAT

Therefore AAT is symmetric because (AT)T = A and AT = AT.

4. Oct 25, 2008