Answer
See solution
Work Step by Step
$det(A)=1$
$det(B)=ad-bc$
$det(A+B)=(1+a)(1+d)-bc=1+a+d+ad-bc$
Thus, $det(A+B)=det(A)+det(B)$ iff $a+d=0$
Linear Algebra and Its Applications (5th Edition)
by Lay, David C.; Lay, Steven R.; McDonald, Judi J.
Published by
Pearson
ISBN 10:
032198238X
ISBN 13:
978-0-32198-238-4
Chapter 3 - Determinants - 3.2 Exercises - Page 178: 42
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