Answer
See answers below
Work Step by Step
a) Computing:
$(A^{-1}B)(B^{-1}A)=A^{-1}(BB^{-1})A=A^{-1}I_nA=A^{-1}A=I_n$
then
$(B^{-1}A)(A^{-1}B)=B^{-1}(AA^{-1})B=B^{-1}I_nB=B^{-1}B=I_n$
Hence, $(B^{-1}A)^{-1}=A^{-1}B$
b) $(A^{-1}B)^{-1}=B^{-1}(A^{-1})^{-1}=B^{-1}A$
