If vmatrix b^2+c^2 & ab & ac ba & c^2+a^2 & bc ca & cb & a^2+b^2 vmatrix is the square of a determinant of the third order then is equal to

JEE Advanced Mathematics question

\begin{vmatrix} b^2+c^2 & ab & ac \\ ba & c^2+a^2 & bc \\ ca & cb & a^2+b^2 \end{vmatrix}

is the square of a determinant of the third order then is equal to

Answer: (A),(C)

Multiply the determinant in (a) by itself, row-by-row: - , , - , -

This gives exactly the given determinant, so (a) works. Its value is

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Question ID VK-108280