Lesson Worksheet: Cayley–Hamilton Theorem Mathematics

In this worksheet, we will practice using the Cayley–Hamilton theorem to solve problems.


Using the Cayley-Hamilton theorem, find 𝐴 for the matrix 𝐴=3154 if possible.

  • A𝐴=1174153
  • B𝐴=4153
  • C𝐴=174153
  • D𝐴=1174153
  • E𝐴=117101511


Using the Cayley-Hamilton theorem, find 𝐴, if possible, for the matrix 𝐴=234556789.

  • A𝐴=14535287103275525
  • B𝐴=14535287103275525
  • CThe matrix has no inverse.
  • D𝐴=14538775510523225
  • E𝐴=156735287103275525


Consider the matrices 𝐴=1234,𝐼=1001.

Find 𝐴.

  • A𝐴=14916
  • B𝐴=14916
  • C𝐴=76922
  • D𝐴=56910
  • E𝐴=7101522

Find 𝐴+3𝐴+2𝐼.

  • A𝐴+3𝐴+2𝐼=64612
  • B𝐴+3𝐴+2𝐼=0000
  • C𝐴+3𝐴+2𝐼=0000
  • D𝐴+3𝐴+2𝐼=41606
  • E𝐴+3𝐴+2𝐼=120012

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