Determinants Matrices Question 128
Question: If A and B are two matrices such that AB = B and BA = A, then $ A^{2}+B^{2} $ is equal to
Options:
A) 2AB
B) 2BA
C) A+B
D) AB
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] We have, $ A^{2}+B^{2}=AA+BB $
$ =A(BA)+B(AB) $
$ (\therefore AB=BandBA+A) $
$ =(AB)A+(BA)B $
$ =BA+AB=A+B(\therefore AB=BandBA=A) $
BETA
