Linear Algebra Done Right · Problem 3C.8

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · matrices-row-column

Problem

Suppose

A

is an

m

-by-

n

matrix and

B

is an

n

-by-

p

matrix. Prove that

(AB)_{j,\cdot} = A_{j,\cdot} B

for each

1 \leq j \leq m

. In other words, show that row

j

AB

equals (row

j

A

) times

B

. This exercise gives the row version of 3.48.