Answer
See answers below
Work Step by Step
a) Given: $AA^T$
To show that $AA^T$ is a symetric matrix, we will use $(AA^T)^T$ and then:
$(AA^T)^T=(A^T)^TA^T=AA^T$
Hence $AA^T$ is a symmetric matrix.
b) Start with $ (ABC)^T$
$ (ABC)^T=[(AB)C]^T=C^T(AB)^T=C^T(B^TA^T)=C^TB^TA^T$
