Matrix multiplication with transpose
No.
Consider block matrices $A = \left(\begin{matrix} 0 &amp; 0 \\ 0 &amp; X \end{matrix}\right)$ (with symmetric $X$) and $B = \left(\begin{matrix} 0 &amp; Y \\ 0 &amp; 0 \end{matrix} \right)$. Computing $AB^T$ from $A$, $B$ and $AB$ means computing $XY^T$ from $X$ and $Y$, since $AB = 0$