A question on minimal polynomial (LA)

by MathematicalPhysicist
Tags: minimal, polynomial
 P: 3,243 f(t)=t^n+a_n-1t^(n-1)+...+a1t+a0 there's a square matrix of order n, A: $$\bordermatrix{ & & & & \cr 0 & 0 & ... & 0& -a_0 \cr 1 &0 & ... & 0 & -a_1 \cr ... & ... & ... & ... & ... \cr 0 & 0 & ... & 1 & -a_{n-1}\cr}$$ show that f(t) is the minimal polynomial of A. i know that f(t) is m.p when f(A)=0, or perhaps all that i should prove here, is that f(t) divides the charectraistic polynomial of A?