A is non singular matrix of order $n$.

Question

Professor PC Thomas Classes · Answer

$$ \begin{align*} & \operatorname{A} \cdot \operatorname{Adj}(A)=|A| I \ & \Rightarrow(\operatorname{Adj}(A))^{-1}=\frac{A}{|A|} \quad(A) ightarrow P, Q \ & \operatorname{Adj}(K A))=K^{n-1} \operatorname{Adj}(A) \quad(B) ightarrow R \ & \operatorname{Adj}(\operatorname{Adj}(K A))=\operatorname{Adj}\left(K^{n-1} \operatorname{Adj}(A)ight)=K^{(n-1)^2} \operatorname{Adj}(\operatorname{Adj}(A))=K^{(n-1)^2}|A|^{n-2} A \quad(C) ightarrow S \ & A^{-1} \cdot \operatorname{Adj}\left(A^{-1}ight)=\left|A^{-1}ight| I=\frac{1}{|A|} I \Rightarrow \operatorname{adj}\left(A^{-1}ight)=\frac{A}{|A|} \quad(D) ightarrow P, Q \end{align*} $$