help find E^2 and E^8 and E^-1 if E is equal to the matrices | 1 0 | | 6 1 |

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help find E^2 and E^8 and E^-1 if E is equal to the matrices | 1 0 | | 6 1 |

Mathematics
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This may be an application of Hamilton-Cayley: characteristic polynomial: X²-2X+1 So E satisfies E²-2E+I=0 [where I is identity matrix and 0 is null matrix] So I=E(2I-E) from where you get E^-1=2I-E [take into account that the matrices E and 2I-E commute] E²=I-2E E^8=E^6-2E^7 [recurrence formula] :)

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