Answer
True
Work Step by Step
We know $A$ and $B$ are matrix functions whose product $AB$ is defined, then $[(AB)^T]_{ij}=(AB)_{ij}\\=\sum^n_{k=1}a_{ji}b_{ki}\\=\sum^n_{k=1}b_{ki}a_{jk}\\=\sum^n_{k=1}b^T_{ik}a^T_{kj}\\=(B^TA^T)_{ij}$
Hence, the matrix functions $(AB)^T$ and $B^T A^T$ are the same.