# 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.

×