Answer
The statement is false.
To make it true, replace "$=A^{-1}B^{-1}$" with
" $=B^{-1}A^{-1}$ ".
Work Step by Step
Since matrix multiplication is associative,
$(AB)(B^{-1}A^{-1})=A(BB^{-1})A^{-1}$
$=AIA^{-1}=AA^{-1}=I$
and
$(B^{-1}A^{-1})(AB)=B^{-1}(A^{-1}A)B$
$=B^{-1}IB=B^{-1}B=I$,
the inverse of $(AB) $ is $(B^{-1}A^{-1})$, not $(A^{-1}B^{-1}).$
The statement is false.
To make it true, replace "$=A^{-1}B^{-1}$"
with
" $=B^{-1}A^{-1}$ ".
