Transpose of matrices

I can interpret two meanings from your question. So, I will explain that two meanings and you can get the one that you are in query.


Case I:

AB^T =/= (A^T)(B^T)

If the equality holds, then A = A^T

in which A =/= A^T in general except when A is symmetric.


Case II:

(AB)^T =/= (A^T)(B^T)

In fact, it can be proved that L.H.S.

(AB)^T = (B^T)(A^T)

in which (B^T)(A^T) =/= (A^T)(B^T) in general.


Conclusion:

Two transpose of matrices cannot multiply together directly.