"Let A, B be n x n matrices. If 3A(B“) is invertible, then both A and B are invertible."

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 86E
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Is this true or false? If true, explain why. If false, provide a counterexample.

Remember - you cannot prove a statement is always true with an example, but you can show a statement
is false by providing an example demonstrating it is false.
"Let A, B be n x n matrices. If 3A(B") is invertible, then both A and B are invertible."
Transcribed Image Text:Remember - you cannot prove a statement is always true with an example, but you can show a statement is false by providing an example demonstrating it is false. "Let A, B be n x n matrices. If 3A(B") is invertible, then both A and B are invertible."
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