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^{5}. Given this how does one calculate the minimal polynomial?

Also just to check, is it correct that the minimal polynomial is the monic polynomial with lowest degree that satisfies M(A)=0 and that all the irreducible factors of the minimal polynomial divide the characteristic polynomial?

Given this I think the minimal polynomial is (1-λ)

^{2}since (I-A)≠0 and (I-A)

^{2}=0 but this method to figure it out seems a little ad hoc.

A=

[1 1 0 0 0]

[0 1 0 0 0]

[0 0 1 1 0]

[0 0 0 1 0]

[0 0 0 0 1]