Suppose that we have \(\displaystyle A_{2,3}~\&~B_{2,3}\) then it impossible to form \(\displaystyle A\cdot B\).
But \(\displaystyle B^T\), the transpose is a \(\displaystyle 3\times 2\) matrix.
Thus \(\displaystyle A\cdot B^T\) is a \(\displaystyle 2\times 2\) matrix.
Well, that would be why I asked, "Why do you ask?" Just trying to make sure we have a good question. If matrices are not conformable, you DON'T multiply them.