If A and B are symmetric matrices of same order such that A B+B A=X and A B-B A=Y, then (X Y)^ T =

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Correct answer: C. -YX

Since X Y=(A B+B A)(A B-B A) =( AB ) AB +( BA )( AB )-( AB )( BA )-( BA )( BA ) Now (X Y)^ T =(( AB ) ( AB ))^ T +( BA AB )^ T - ( AB BA )^ T array r =( AB )^ T ( AB )^ T +( AB )^ T ( BA )^ T -( BA )^ T ( AB )^ T \ -( BA )^ T ( BA )^ T array = (B^ A^ ) (B^ A^ )+ (B^ A^ ) (A^ B^ ) - ( A ^ B ^ ) ( B ^ A ^ )- ( A ^ B ^ ) ( A ^ B ^ ) Since, A & B are symmetric matrix. =( BA )( BA )+( BA )( AB )-( AB )( BA ) -( AB )( AB ) =( BA - AB )( BA + AB )=- YX

BITSAT Mathematics Question (2024) — Solution

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