Grade 12th passAlgebra
if A&B are two square matrices such that B= -A-1BA, then prove that ( A+B)2=A2+B2
if A&B are two square matrices such that B= -A-1BA, then prove that ( A+B)2=A2+B2
2 Answers
Amit Sharma
Approved Tutor Answer8 Years agoIt 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
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)}Other Related Questions on algebra
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