A First Course in Linear Algebra · Problem CRS.T41

Matrices — Robert Beezer

Mathematics — Linear Algebra · column-space-nonsingular-product

Problem

Suppose that

A

is an

m \times n

matrix and

B

is an

n \times n

nonsingular matrix. Prove that the column space of

A

is equal to the column space of

AB

, that is

\mathcal{C}(A) = \mathcal{C}(AB)