Matrices And Determinants

If $A, B$ are two non singular matrices of order $3,|B|=k$, a positive integer, then match the items of list-I with the items of list-II.

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\( \text { List-I } \)		\( \text { List-II } \)
A.	$\quad\left|k^{-1} A^{-1}\right|$	I.	\( B A^k+A^k B \)
B.	$\left|\operatorname{Adj}\left(A^{-1}\right)\right|$	II.	\( \frac{B \operatorname{Adj}(B)}{|B|} \)
C.	$B A B^{-1}=I, \Rightarrow B A^k B^{-1}=$	III.	\( \frac{1}{|B|^3|A|} \)
D.	$\quad \operatorname{Adj}\left(\operatorname{Adj}\left(A^{-1}\right)\right)=$	IV.	\( \frac{1}{|A|}\left(A^{-1}\right) \)
		V.	\( \frac{1}{|A|^2} \)

\(\text { The correct match is }\)