Practice problem with invertible matrices

[myusernameis]

Simplify: (B$$^{-1}$$A$$^{T}$$)$$^{-1}$$B$$^{-1}$$(ABA)$$^{T}$$((AB)$$^{T}$$)$$^{-1}$$

Is the answer 1?

thx

 

[trambolin]

Yep,
$$A^{-T}B \ \ B^{-1}\ \ A^TB^TA^T \ \ A^{-T}B^{-t} = I$$