Answer
This addition of a scalar multiple of row 2 to row 1 does not change the determinant.
Work Step by Step
$\begin{vmatrix}a&b\\c&d\end{vmatrix}=ad-bc=(ad-bc)+(kcd-kcd)=(ad+kcd)-(bc+kcd)=\begin{vmatrix}a+kc&b+kd\\c&d\end{vmatrix}$
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