Suppose A is an m x matrix and B is an n x p matrix. If AB has full rank, then A and B both have full rank. O True O False

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.4: Determinants
Problem 53PS
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If the statement in the image is true, is there a proof or if its false is there a counterexample?

Suppose A is an m x matrix and B is an n x p matrix. If AB has full rank, then A and B both
have full rank.
True
False
Transcribed Image Text:Suppose A is an m x matrix and B is an n x p matrix. If AB has full rank, then A and B both have full rank. True False
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