Answer
False
Work Step by Step
Let $A$ be the non zero matrix and assume $B=-A$
then $A+B=0 \Leftrightarrow rank(A+B)=0$
Since $rank(A),rank (B)\geq 1$, we have $rank(A)+rank(B)\geq 2$
Hence, the statement is false.
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 - 2.4 Row-Echelon Matrices and Elementary Row Operations - True-False Review - Page 155: e
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