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: