Question

Let $A$ be a non-singular matrix. Then $\left|adjA\right|$ is equal to

• A. ${\left|A\right|}^n$
• B. ${\left|A\right|}^{n-1}$
• C. ${\left|A\right|}^{n-2}$
• D. None of these

Answer 1

Answer: (B)

${\left|A\right|}^{n-1}$

Since A is non-singular

$\therefore A^{-1}$ exists

Now ,$A$ $\left(adjA\right)$=$\left|A\right|I=$$\left(adjA\right)A$

$\Rightarrow \left|A\right|\left|adjA\right|={\left|A\right|}^n=\left|adjA\right|\left|A\right|$

$\therefore \left|adjA\right|={\left|A\right|}^{n-1}$