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Problem: Is Nilpotent matrix [[1,2,3],[1,2,3],[-1,-2,-3]] [ Calculator, Method and examples ]

Solution:
Your problem `->` Is Nilpotent matrix [[1,2,3],[1,2,3],[-1,-2,-3]]


A square matrix `A` is called a nilpotent matrix, if `A^m = 0` for some positive integer m.


`A` = 
`1``2``3`
`1``2``3`
`-1``-2``-3`


`A×A`=
`1``2``3`
`1``2``3`
`-1``-2``-3`
×
`1``2``3`
`1``2``3`
`-1``-2``-3`


=
`1×1+2×1+3×-1``1×2+2×2+3×-2``1×3+2×3+3×-3`
`1×1+2×1+3×-1``1×2+2×2+3×-2``1×3+2×3+3×-3`
`-1×1-2×1-3×-1``-1×2-2×2-3×-2``-1×3-2×3-3×-3`


=
`1+2-3``2+4-6``3+6-9`
`1+2-3``2+4-6``3+6-9`
`-1-2+3``-2-4+6``-3-6+9`


=
`0``0``0`
`0``0``0`
`0``0``0`



Here `A^2 = 0`, so `A` is a nilpotent matrix whose index is 2








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