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What is the value of a determinant having two identical rows?

  • A.unity
  • B.twice the value of either row's cofactor sum
  • C.equal to the product of the diagonal entries
  • D.zero

Answer: D

Interchanging the identical rows must change the sign while leaving the determinant unaltered, and only zero satisfies both. The same conclusion follows from the rows being linearly dependent, which makes the matrix singular.

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