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CBSE Class 12-commerce Answered

1) If A , B and AB are symmetric matrices, then show AB=BA 2) If A,B are Skew symmetric matrices and AB=BA, then show that AB is symmetric 3) If A,B are Skew symmetric matrices of same order and AB is Symmetric , show that AB=BA
Asked by drawing13334 | 31 Aug, 2018, 10:33: AM
answered-by-expert Expert Answer
begin mathsize 16px style If space straight A space comma space straight B space and space AB space are space symmetric space matrices comma space then space show space AB equals BA
Proof colon
AB space equals space open parentheses AB close parentheses to the power of straight T space....... left parenthesis 1 right parenthesis open parentheses since space AB space is space straight a space symmetric space matrices close parentheses
but space space open parentheses AB close parentheses to the power of straight T space equals straight B to the power of straight T space straight A to the power of straight T space space space.... left parenthesis 2 right parenthesis space space space space
We space have space straight A to the power of straight T space equals space straight A space and space straight B to the power of straight T space equals space straight B space space space space......... left parenthesis 3 right parenthesis left parenthesis straight A space and space straight B space are space symmetric space matrices right parenthesis
from space left parenthesis 2 right parenthesis space space bold space open parentheses AB close parentheses to the power of straight T space equals straight B to the power of straight T space straight A to the power of straight T space space space space
space space space space space space space space space space space space space space space space space space AB space equals space BA....... space from space left parenthesis 1 right parenthesis space and space left parenthesis 3 right parenthesis

end style
Answered by Yasmeen Khan | 31 Aug, 2018, 11:02: AM
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