Linear Algebra Done Right · Problem 3C.15

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · transpose

Problem

Prove that if

A

is an

m

-by-

n

matrix and

C

is an

n

-by-

p

matrix, then

(AC)^{\mathrm{t}} = C^{\mathrm{t}} A^{\mathrm{t}}.

This exercise shows that the transpose of the product of two matrices is the product of the transposes in the opposite order.