Don't get scared by the expression!

If $A$ and $B$ are non-singular square matrices such that $A$ is symmetric and $B$ is skew symmetric and also $AB=BA$ then simplify the following expression: ${ A }^{ 3 }{ B }^{ 3 }{ ({ B }^{ T }A) }^{ -1 }{ ({ A }^{ -1 }{ B }^{ -1 }) }^{ T }AB$

Note : ${ M }^{ T }$ and ${ M }^{ -1 }$ refer to the transpose and inverse of matrix $M$ respectively.