If A and B are square matrices of same order satisfying A+B=AB, then
A
AB=BA
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
AB=−BA
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
A+B=−BA
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
A−B=BA
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is AAB=BA Given, A+B=AB⋯(1) ⇒AB−A−B+I=I ⇒(I−A)(I−B)=I ⇒I−A and I−B are inverse of each other.
So, (I−B)(I−A)=I ⇒I−A−B+BA=I ⇒A+B=BA⋯(2)