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## Homework Statement

Let

*V*be the vector space of

*n x n*matrices over the field

*F*. Fix [tex] A \in V[/tex]. Let

*T*be the linear operator on

*V*defined by

*T(B) = AB*, for all [tex] B \in V[/tex].

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 [tex]\left\{E_{ij} \right| 1 \leq i,j \leq n [/tex]}, where [tex]E_{ij}[/tex] is the matrix having 1 in the (i,j)th entry and zeros everywhere else.

## Homework Equations

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## 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...