More fun in 2016, Part 19

Algebra Level 4

How many real \(3\times 3\) matrices \(A\) are there such that \(A^{2016}=-I_3\), where \(I_3\) represents the \(3\times 3\) identity matrix.

Enter 666 if you come to the conclusion that infinitely many such matrices \(A\) exist.

Hint: Use determinants.


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