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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

Options

  1. AS
  2. BB C D
  3. CS T
  4. DS T 2 = S 2 T

Correct answer

D. S T 2 = S 2 T

Step-by-step solution

Given C T = D A B ,   D T = A B C ,   S = A B C D Using S T = A B C D T = D T C T B T A T , We get S T 2 = D T C T B T A T 2 = D T C T B T A T D T C T B T A T = D T C T D A B T A B C T = D T C T C D And, S 2 T = A B C ⏟ D A B ⏟ C D T = D T C T C D Hence, S T 2 = S 2 T

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