Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 2 - Matrices and Systems of Linear Equations - 2.7 Elementary Matrices and the LU Factorization - Problems - Page 188: 28

Answer

See below

Work Step by Step

If $P = P_1P_2 ... P_k$, where each $P_i$ is an elementary permutation matrix then $P_i=P_i^{-1}=P_i^T$ Thus, $P^{-1}\\=(P_1P_2..P_k)^{-1}\\=P_k^{-1}...P_2^{-1}P_k^{-1}\\=P_k^T....P_2^TP_1^T\\=(P_1P_2...P_k)^T\\=P^T$
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