Recent content by darksidemath

Hi guys i have this problem in my linear algebra curse . let $T:\mathbb{Q}^3→\mathbb{Q}^3$ a linear application s.t $(T^7+2I)(T^2+3T+2I)^2=0$ can you find all possible Jordan forms of T and related characteristic polynomial ? I am totally lost and that is the first time i see this type of problem

let p∈Z a prime how can I show that p is a prime element of Z[√3] if and only if the polynomial x^2−3 is irreducible in Fp[x]? ideas or everything is well accepted :)