$ABCD = I$ 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 ?

Since A, B, C, D all have non zero determinant this implies that their respective inverses exist.
It's really an exercise in matrix algebra and in particular matrix multiplication.
\begin{align}
ABCD &=I\\
AB &=D^{-1}C^{-1}\\
B &=A^{-1}D^{-1}C^{-1}\\
B^{-1} &=CDA
\end{align}
