Question

If $I$ is the unit matrix of order $n$, where $k\ne 0$ is a constant then $\text{adj}\left(kI\right)=$

• A. $k^n\left(\text{adj}I\right)$
• B. $k\left(\text{adj}I\right)$
• C. $k^2\left(\text{adj}I\right)$
• D. $k^{n-1}\left(\text{adj}I\right)$

Answer 1

Answer: (D)

$k^{n-1}\left(\text{adj}I\right)$

Given that $I$ is unit matrix of order $n$

Consider $\text{adj}\left(kI\right)$ , each term in the diagonal is equal to $k^{n-1}$ and all the remaining terms are zeros.

Therefore $\text{adj}\left(kI\right)=k^{n-1}\left(adjI\right)$

So the correct option is $D$