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Matriceshard
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Let AAA be a 3×33 \times 33×3 matrix with tr(A)=3\text{tr}(A) = 3tr(A)=3, tr(A2)=5\text{tr}(A^2) = 5tr(A2)=5, and tr(A3)=7\text{tr}(A^3) = 7tr(A3)=7. What is the determinant of AAA?