If \(\left| {\begin{array}{*{20}{c}} {\rm{x}}&{\rm{y}}&0\\ 0&{\rm{x}}&{\rm{y}}\\ {\rm{y}}&0&{\rm{x}} \end{array}} \right| = 0\), then which one of the following is correct?

\(\frac{{\rm{x}}}{{\rm{y}}}\) is one of the cube roots of unity

x is one of the cube roots of unity

y is one of the cube roots of unity

\(\frac{{\rm{x}}}{{\rm{y}}}\) is one of the cube roots of -1

If \(\left| {\begin{array}{*{20}{c}} {\rm{x}}&{\rm{y}}&0\\ 0&{\rm{x}}&

1.	If \(\left\| {\begin{array}{*{20}{c}} {\rm{x}}&{\rm{y}}&0\\ 0&{\rm{x}}&{\rm{y}}\\ {\rm{y}}&0&{\rm{x}} \end{array}} \right\| = 0\), then which one of the following is correct?
A.	\(\frac{{\rm{x}}}{{\rm{y}}}\) is one of the cube roots of unity
B.	x is one of the cube roots of unity
C.	y is one of the cube roots of unity
D.	\(\frac{{\rm{x}}}{{\rm{y}}}\) is one of the cube roots of -1
Answer» E.

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If \(\left| {\begin{array}{*{20}{c}} {\rm{x}}&{\rm{y}}&0\\ 0&{\rm{x}}&{\rm{y}}\\ {\rm{y}}&0&{\rm{x}} \end{array}} \right| = 0\), then which one of the following is correct?

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