Let A,B,C,D be square real matrices such that C^T=DAB, D^T=ABC, S=ABCD, then S^2 is equal to

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Correct answer: (D) ST^2=S2^T. Given C^T=DAB, D^T=ABC, S=ABCD Using S^T=ABCD^T=D^TC^TB^TA^T, We get ST^2=DTCTBTAT^2 =D^TC^TB^TA^TD^TC^TB^TA^T =D^TC^TDAB^TABC^T =D^TC^TCD And, S2^T=ABC⏟DAB⏟CD^T =D^TC^TCD Hence, ST^2=S2^T

Let $A, B, C, D$ be square real matrices such that $C^{T} = D A B, D^{T} = A B C, S = A B C D$ , then $S^{2}$ is equal to

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Relevant Questions

Let A,B,C,D be square real matrices such that CT=DAB, DT=ABC, S=ABCD, then S2 is equal to

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Relevant Questions

Let $A, B, C, D$ be square real matrices such that $C^{T} = D A B, D^{T} = A B C, S = A B C D$ , then $S^{2}$ is equal to