Linear Algebra and Its Applications · Problem 1.4.10

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · matrix-notation-and-multiplication

Problem

True or false? Give a specific counterexample when false. (a) If columns 1 and 3 of

B

are the same, so are columns 1 and 3 of

AB

. (b) If rows 1 and 3 of

B

are the same, so are rows 1 and 3 of

AB

. (c) If rows 1 and 3 of

A

are the same, so are rows 1 and 3 of

AB

. (d)

(AB)^2 = A^2B^2