A) \[3-x+y\]
B) \[(1-x)(1+y)\]
C) \[xy\]
D) \[-xy\]
Correct Answer: D
Solution :
\[\left| \,\begin{matrix} 1 & 1 & 1 \\ 1 & 1-x & 1 \\ 1 & 1 & 1+y \\ \end{matrix}\, \right|=\left| \,\begin{matrix} 1 & 0 & 0 \\ 1 & -x & x \\ 1 & 0 & y \\ \end{matrix}\, \right|=-xy\].
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