Don't get scared by the expression!

Algebra Level 3

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.

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