Answer
See below.
Work Step by Step
Assume the statement is false. Then $a\ne0$ and $b\ne0$. But then $(a+b)^2=a^2+b^2+2ab$ in which $2ab\ne0$, thus $(a+b)^2\ne a^2+b^2$, but this is a contradiction. Thus the statement is true.
Elementary Linear Algebra 7th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
1-13311-087-8
ISBN 13:
978-1-13311-087-3
Appendix - Mathematical Induction and Other Forms of Proofs - Exercises - Page A6: 17
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