Answer
False
Work Step by Step
If $AB$ is upper triangular then it is not necessary that both $A$ and $B$ are upper triangular.
Here on the right $AB$ is zero matrix so it is upper triangular. But $A$ and $B$ are not upper triangular.
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 2 - Matrices and Systems of Linear Equations - 2.2 Matrix Algebra - True-False Review - Page 134: g
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