Linear Algebra and Its Applications · Problem 2.4.5

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

If the product

AB

is the zero matrix,

AB = 0

, show that the column space of

B

is contained in the nullspace of

A

. (Also the row space of

A

is in the left nullspace of

B

, since each row of

A

multiplies

B

to give a zero row.)