16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 5.2.9

Determinants

Mathematics — Linear Algebra · alternating-n-linear-functions

Problem

Let

K

be a commutative ring with identity and

D

an alternating

n

-linear function on

n \times n

matrices over

K

. Show that ((a))

D(A) = 0

, if one of the rows of

A

0

. ((b))

D(B) = D(A)

, if

B

is obtained from

A

by adding a scalar multiple of one row of

A

to another.