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If $k$ is a scalar and $/$ is a unit matrix of order 3 , then $\operatorname{adj}(k I)=$
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Verified Answer
The correct answer is:
$k^2 I$
Let $I=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$, then $k I=\left[\begin{array}{lll}k & 0 & 0 \\ 0 & k & 0 \\ 0 & 0 & k\end{array}\right]$
$\Rightarrow \operatorname{adj}(k I)=\left[\begin{array}{ccc}k^2 & 0 & 0 \\ 0 & k^2 & 0 \\ 0 & 0 & k^2\end{array}\right]=k^2 I$.
$\Rightarrow \operatorname{adj}(k I)=\left[\begin{array}{ccc}k^2 & 0 & 0 \\ 0 & k^2 & 0 \\ 0 & 0 & k^2\end{array}\right]=k^2 I$.
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