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 ,…

Let A,B,C,D be square real matrices such that CT=DAB, DT=ABC, S=ABCD, then S2 is equal to
  1. S
  2. BCD
  3. ST
  4. ST2=S2T

Solution

Given CT=DAB, DT=ABC, S=ABCD

Using ST=ABCDT=DTCTBTAT, We get

ST2=DTCTBTAT2

=DTCTBTATDTCTBTAT

=DTCTDABTABCT

=DTCTCD

And, S2T=ABC⏟DAB⏟CDT

=DTCTCD

Hence, ST2=S2T

Asked in: AP EAMCET 2021 (19 Aug Shift 2)

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