Prove that if both products AB and BA are defined, then AB and BA are square matrices. Assume that A is an m xn matrix and B is a p xq matrix. Because AB is defined, you have that ---Select-- v and AB is a(n) -Select-- v matrix. Because BA is defined, you have that -Select-- v and so AB is an --Select- v square matrix. Likewise, because BA is defined, --Select- v and BA is a(n) ---Select--- v matrix. Because AB is defined, you have -Select-- v Therefore, BA is an-Select-v square matrix.
Prove that if both products AB and BA are defined, then AB and BA are square matrices. Assume that A is an m xn matrix and B is a p xq matrix. Because AB is defined, you have that ---Select-- v and AB is a(n) -Select-- v matrix. Because BA is defined, you have that -Select-- v and so AB is an --Select- v square matrix. Likewise, because BA is defined, --Select- v and BA is a(n) ---Select--- v matrix. Because AB is defined, you have -Select-- v Therefore, BA is an-Select-v square matrix.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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