Which among the following would be obtained on simplifying the expression (ATBA)T.
A
ATBTAT
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B
ATBTA
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C
AATBT
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D
BTATA
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Solution
The correct option is BATBTA The main principle that has to be applied is, (XY)T=YT.XT. Using this in our present case, (ATBA)T=(BA)T.(AT)T =ATBTA
Note that in the first step we group the terms in the expression to AT and BA to apply this law.