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Q.

Let A, B.C, D be (not necessarily) real matrices such that AT=BCD;BT=CDA;CT=DAB and DT=ABC for the matrix S = ABCD, the least value of k such that Sk = S is

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answer is 3.

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Detailed Solution

S=ABCD=A(BCD)=AAT∴ S3=(ABCD)(ABCD)(ABCD)=(ABC)(DAB)(CDA)(BCD)=DTCTBTAT=(BCD)TAT=ATTAT=AAT=S⇒ S3=SHence, least value of k is 3.
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