if A&B are two square matrices such that B= -A-1BA, then prove that ( A+B)2=A2+B2
shreyansh , 6 Years ago
Grade 12th pass
Algebra> if A&B are two square matrices such that ...
2 Answers
Amit Sharma
Last Activity: 6 Years ago
It is given that
B = -A-1BA
now, pre-multiplying by A on both sides, we will get
AB = -BA
AB+BA = 0.........................(1)
Now coming to the problem:
(A+B)2=(A+B)*(A+B) = A2+B2+AB+BA.....................(2)
(A+B)2=(A+B)*(A+B) = A2+B2+AB+BA.....................(2)
from (1) and (2), we get
(A+B)2=(A+B)*(A+B)
Amit Sharma
Last Activity: 6 Years ago
It is given that
B = -A-1BA
now, pre-multiplying by A on both sides, we will get
AB = -BA
AB+BA = 0.........................(1)
Now coming to the problem:
(A+B)2=(A+B)*(A+B) = A2+B2+AB+BA.....................(2)
(A+B)2=(A+B)*(A+B) = A2+B2+AB+BA.....................(2)
from (1) and (2), we get
( A+B)2=A2+B2 as AB+BA =0 {from (1)}Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on Algebra
Can we divide two vectors? If this is possible then how?
Algebra
1 Answer Available
Last Activity: 10 Month ago(s)
How do you write “the product of 18 and q” as an algebraic expression?
Algebra
1 Answer Available
Last Activity: 10 Month ago(s)
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
Algebra
0 Answer Available
Last Activity: 1 Year ago(s)