Question

If k is a scalar and I is a unit matrix of order 3, then adj(kI) =

• A. k³I
• B. k²I
• C. - k³I
• D. - k²I

Answer 1

The correct option is B

k²I

$\begin{array}{c}LetI=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right],thenkI=\left[\begin{array}{ccc}k& 0& 0\\ 0& k& 0\\ 0& 0& k\end{array}\right]\end{array}$

$\Rightarrow \begin{array}{c}adj\left(kI\right)=\left[\begin{array}{ccc}{k}^2& 0& 0\\ 0& k^2& 0\\ 0& 0& k^2\end{array}\right]=k^{2}I\end{array}$