1.4.32 Matrix transformations

Condition: Is it possible to reduce the transposition of a general matrix to the operations of multiplying it on the left and on the right by any predetermined matrices? In other words, are there matrices \( A \) and \( B \) for which the equality \( A X B=X^{T} \) holds for any matrix \( X \in \mathbb{R}^{m \times n} \)?