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Why is matrix multiplication described as non-commutative?

  • A.AB and BA are always equal for square matrices
  • B.the operation is undefined for square matrices
  • C.the operation reverses the sign of the determinant
  • D.AB and BA generally differ, and may not both exist

Answer: D

The number of columns of the first must match the rows of the second, so one product may exist while the other does not, and even for square matrices the two results usually differ. It is the single most important respect in which matrix algebra departs from ordinary arithmetic.

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