16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 5.4.6

Determinants

Mathematics — Linear Algebra · determinant-linear-operators

Problem

Let

T

and

U

be linear operators on the finite dimensional vector space

V

. Prove ((a))

\det(TU) = (\det T)(\det U)

; ((b))

T

is invertible if and only if

\det T \neq 0