Question

If $A$ is a matrix of order $3$, such that $A(adjA)=10I$, then $|adjA|$ =

• A. $10$
• B. $10I$
• C. $1$
• D. $100$

Answer 1

Answer: (D)

Given, $A(adjA)=10I$
We know, $A(adjA)=|A|I$
$\therefore 10I=|A|I$
$\Rightarrow |A|=10$
$\therefore \mid$ adj ${A|=|A|}^{3-1}=(10{)}^2=100$