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Let A, B, C, D be (not necessarily squar...

Let A, B, C, D be (not necessarily square) real matrices such that `A^T=BCD: B^T=CDA; C^T=DAB` and `D^T=ABC.` For the matrix `S=ABCD`, consider the two statements. I. `S^3=S` II. `S^2=S^4` (A) II is true but not I (B) I is true but not II (C) both I and II are true (D) both I and II are false

Text Solution

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`S^T=(ABCD)^T=D^TC^TB^TA^T`
`=ABC*DAB*CDA*BCD`
`S^T=S^3`
`S^4=S^3*S=S^T*s!=s^2`
option d is correct.
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