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

Explanation

`S=ABCD=A(BCD)=A A^(T)`
`S^(3)=(ABCD) (ABCD) (ABCD)`
`=(ABC)(DAB)(CDA)(BCD)`
`=D^(T)C^(T)B^(T)A^(T)`
`=(BCD)^(T)A^(T)=A A^(T)`
From (1) and (2), `S=S^(3)`