16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 5.4.8

Determinants

Mathematics — Linear Algebra · determinant-commutator-operator

Problem

Let

V

be the vector space of

n \times n

matrices over the field

F

. Let

B

be a fixed element of

V

and let

T_B

be the linear operator on

V

defined by

T_B(A) = AB - BA

. Show that

\det T_B = 0