What is the minimal polynomial for T and A?

[CoachZ]

Homework Statement

Let V be the vector space of n x n matrices over the field F. Fix $$A \in V$$. Let T be the linear operator on V defined by T(B) = AB, for all $$B \in V$$.

a). Show that the minimal polynomial for T equals the minimal polynomial for A.
b) Find the matrix of T with respect the the standard basis of V. i.e. the basis $$\left\{E_{ij} \right| 1 \leq i,j \leq n$$}, where $$E_{ij}$$ is the matrix having 1 in the (i,j)th entry and zeros everywhere else.

Homework Equations

...

The Attempt at a Solution

I know that the operator T is represented in some ordered basis by the matrix A, then T and A have the same minimal polynomial. The problem I'm running into is that I'm having a really hard time understanding abstract linear algebra, so this is all very very confusing to me and I'm not quite sure where to even start on this problem...

 

[HallsofIvy]

What is the definition of "minimal polynomial" for a linear operator?