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

Question

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, S, B C D, S T, S T 2 = S 2 T

MARKS App · Accepted Answer

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

Search any question & find its solution

Looking for more such questions to practice?