If A= bmatrix y & z & x z & x & y x & y & z bmatrix where x, y, z are integers, is an orthogonal matrix, then what is the value of x^2+y^2+z^2?

NDA 2025 Mathematics question

where are integers, is an orthogonal matrix, then what is the value of ?

Answer: (B)

For an orthogonal matrix, . The entry of is the dot product of the first row with itself:

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Question ID VK-030035