$ABCD = I$ then $B^{-1} =?$ I got this question in a practice book.
A,B,C and D are $n\times n$ matrices with non-zero determinant.
$ABCD = I$ , then $B^{-1}$ = ?
The answer to this was $B^{-1}= CDA$. 
How was that answer arrived at ?

If $ABCD = I$, then $BCD = A^{-1}$, $BC = A^{-1}D^{-1}$, $B = A^{-1}D^{-1}C^{-1}$,
from which we get $B^{-1} = (A^{-1}D^{-1}C^{-1})^{-1} = CDA$.
