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- 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: A
- [ 0 0 -3]
- [ 1 0 6]
- [ 0 1 -3]
- sage: A.characteristic_polynomial()
- x^3 + 3*x^2 - 6*x + 3
- sage: (1/A^2)
- [ 3 2 1]
- [-7/3 -1 0]
- [-2/3 -1/3 0]
- sage: (1/A^2).characteristic_polynomial()
- x^3 - 2*x^2 + 7/3*x - 1/9
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