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Give an example of a $4 \times 4$ matrix where $A \neq I$, $A^2 \neq I$, and $A^3 = I$.

I found a $2 \times 2$ matrix where $A \neq I$ and $A^2 = I$, but this problem is more complex and has me completely stumped.

  • 0
    Sure! Will certainly do.2012-10-03
  • 1
    Does it have to be a real matrix? Have you heard of rotation matrices?2012-10-03
  • 0
    I think it can be any type of matrix.2012-10-03
  • 1
    If $A\neq I$ and $A^3=I$, then it's not possible for $A^2$ to equal $I$. So it's not necessary to include the condition $A^2\neq I$.2012-10-03

6 Answers 6