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transgalactic

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S:R3[x]->R3[x]

and we have the polinomial from which we take the eigenvalues from

t^3 - 4t

find wether S invertable or not?i tried to think about that and i got that the aigenvalues are 2 , 0, -2

but that only prooves that it diagonizable

i know a law that if the determinant differs zero then its invertable

but i don't know how to apply it here

?