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Which property characterises an orthogonal matrix?

  • A.its determinant is zero
  • B.all its entries are either zero or one
  • C.its transpose is its inverse
  • D.its transpose equals the matrix itself

Answer: C

The condition means the rows form an orthonormal set, so the matrix preserves lengths and angles under the transformation it represents. Its determinant is therefore plus or minus one, corresponding to a rotation or a rotation with a reflection.

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