A matrix A Mat n R is symmetric if A = A t and skew-symmetric if
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A matrix A ϵ MatnR is symmetric if A = At and skew-symmetric if A = -At.
(a) If A and B are [skew] symmetric, then A +B is [skew] symmetric.
(b) Let R be commutative. If A,B are symmetric, then AB is symmetric if and only if AB = BA. Also show that for any matrix B ϵ MatnR,BBt and B + Bt are symmetric and B - Bt is skew-symmetric.
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a If A and B are skew symmetric then A B is skew symmetric This statement is true Lets consider the ...View the full answer
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Related Book For 
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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