wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If A and B are two square matrices such that B=−A−1BA, then (A+B)2 is equal to

A
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
A2+B2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
A2+2AB+B2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
A+B
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B A2+B2
As B=A1BA, we get AB = -BA or AB + BA = 0.
Now,
(A+B)2=(A+B)(A+B)
=A2+BA+AB+B2
=A2+O+B2
=A2+B2.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adjoint and Inverse of a Matrix
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon