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What does the Cayley-Hamilton theorem assert?

  • A.the trace of a matrix equals its determinant
  • B.a matrix satisfies its own characteristic equation
  • C.a matrix commutes with its own transpose
  • D.the eigenvalues of a matrix are always real

Answer: B

Substituting the matrix into its characteristic polynomial gives the zero matrix, which allows high powers to be reduced and the inverse to be expressed as a polynomial in the matrix. It is a standard route to computing an inverse without cofactors.

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