x+y000x-y000x2+y2 ⇒(x+y) x-y x2+y2-0 =x2-y2 x2+y2 = x4-y4

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$|\begin{matrix} x + y & 0 & 0 \\ 0 & x - y & 0 \\ 0 & 0 & x^{2} + y^{2} \end{matrix}| =$

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$x^{4} - y^{4}$

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answer is A.

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Detailed Solution

$\begin{array}{rcl} |\begin{matrix} x + y & 0 & 0 \\ 0 & x - y & 0 \\ 0 & 0 & x^{2} + y^{2} \end{matrix}| & \Rightarrow & (x + y) ((x - y) (x^{2} + y^{2}) - 0) \\ = & (x^{2} - y^{2}) (x^{2} + y^{2}) \\ = & x^{4} - y^{4} \end{array}$

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