Question

If $A\left(adjA\right)=5I$ where $I$ is the identity matrix of order $3$, then $|adjA|$ is equal to

• A. $125$
• B. $25$
• C. $5$
• D. $10$

Answer 1

Answer: (B)

$25$

$A.A^{-1}=IA.\frac{1}{|A|}\left(adjA\right)=IA.\left(adjA\right)=|A|I$

Comparing the above expression with the given expression

$|A|=5$

$adjA=|A|A^{-1}|adjA|=||A|A^{-1}|={|A|}^2=25$