Question

If $A$ is matrix of order $3$, such that $A\left(adjA\right)=10I$, then |adj A|=

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

Answer 1

The correct option is D $100$

Consider the following identity $A\left(adjA\right)=|A|I$. Thus comparing it with the above equation gives us $|A|=10$
Now $|adjA|=|A{|}^{n-1}$ where n is the order of the square matrix.
Here 'n' is 3, therefore, $|adjA|=|A{|}^{3-1}=|A{|}^2={10}^2=100$.