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# If $A$ is a scalar matrix with scalar $k \neq 0$ of order $3$ than $A^{-1}$ is

$\begin{array} {1 1}(1)\frac{1}{k^{2}}I&(2)\frac{1}{k^{3}}I\\(3)\frac{1}{k}I&(4)kI\end{array}$

$A=\begin{bmatrix} K & 0 & 0 \\ 0 & K & 0 \\ 0 & 0 & K \end{bmatrix}$
$A^{-1}= \large\frac{1}{|A|} $$adj A Co factor matrix of A=\begin{bmatrix} K^2 & 0 & 0 \\ 0 & K^2 & 0 \\ 0 & 0 & K^2 \end{bmatrix} |A|=K^3 A^{-1}=\large\frac{1}{K^3}$$ K^2 \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$
$\qquad =\large\frac{1}{K}$$I$
Hence 3 is the correct answer.