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Let x, y and z be complex numbers. If Δ denotes the determinant of the matrix [0, -y, -z; y, 0, -x; z, x, 0], then Δ is

1. purely real
2. purely imaginary
3. complex
4. zero

Correct answer: zero

Solution

The matrix is skew-symmetric (M^T = -M) and of odd order 3. For an odd-order skew-symmetric matrix det = 0; direct expansion of [[0,-y,-z],[y,0,-x],[z,x,0]] also gives 0.

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