For a non-singular $n imes n$ matrix $A$, the relation between $\det…

Question

For a non-singular $n 	imes n$ matrix $A$, the relation between $\det(\operatorname{adj} A)$ and $\det A$ is:

Accepted Answer

C. $|\operatorname{adj} A| = |A|^{n-1}$

From $A\,\operatorname{adj}(A) = |A| I_n$, taking determinants: $|A| \cdot |\operatorname{adj}(A)| = |A|^n$. Hence $|\operatorname{adj}(A)| = |A|^{n-1}$ when $|A| 
e 0$.

Answer

$|\operatorname{adj} A| = |A|$

Answer

$|\operatorname{adj} A| = |A|^{n}$

Answer

$|\operatorname{adj} A| = \dfrac{1}{|A|}$

For a non-singular $n \times n$ matrix $A$, the relation between $\det(\operatorname{adj} A)$ and $\det A$ is: