M: V -> V linear operator st M^2 + 1_v = 0
find the POSSIBILITIES for min. pol. of M^3+2M^2+M+3I_v
The Attempt at a Solution
using M^2 = -1_v,
i rewrote the operator(?) as
M^3 + M + I_v
i dunno what to do. i guessed min poly to be like x^3-x-1
but what would be other possibilities. i seriously doubt the one i guessed is even correct.
i know that, if min poly is u(x) then u(M) = 0.