box% sage ┌────────────────────────────────────────────────────────────────────┐ │ SageMath version 9.2, Release Date: 2020-10-24 │ │ Using Python 3.8.6. Type "help()" for help. │ └────────────────────────────────────────────────────────────────────┘ sage: A = matrix([[0,0,-3],[1,0,6],[0,1,-3]]) sage: (1/A^2).characteristic_polynomial() # 3.1 x^3 - 2*x^2 + 7/3*x - 1/9 sage: (A^2).characteristic_polynomial() # 3.2 x^3 - 21*x^2 + 18*x - 9 sage:
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