If A is non - singular matrix of order $\mathrm{n}\times \mathrm{n}$,

	Column 1		Column 2
(A)	$adj \left(A^{-1}\right) is$	(P)	A (det A)n-2
(B)	$det (adj (A^{-1}\left)\right) is$	(Q)	(det A)n-1(adj A)
(C)	$adj (adj A) is$	(R)	$\frac{adj (adj A)}{{(det A)}^{n-1}}$
(D)	$adj (A det (A\left)\right) is$	(S) (T)	${\left(det A\right)}^{1-n}$ $\frac{A}{\left(det A\right)}$

$$\begin{gathered} \left(A\right)=(R,T); \left(B\right)=\left(S\right); \left(C\right) =\left(P\right); \left(D\right) =\left(Q\right) \\ \left(A\right) adj \left(A^{-1}\right)={\left(A^{-1}\right)}^{-1}det\left(A^{-1}\right)=\frac{A}{det\left(A\right)} \\ \left(B\right) det (adj A^{-1}))={(det A^{-1})}^{n-1} \\ =\frac{1}{{(det A)}^{n-1}}={(det A)}^{1-n} \\ (C) adj [adj A]=A{(det A)}^{n-2} \\ (D) adj(A det A)={(det A)}^{n-1}(adj A) \end{gathered}$$