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  • Choose the correct answer in the Exercises 11 and 12. If A, B are symmetric matrices of same order, then AB minus BA is a (A) Skew symmetric matrix (B) Symmetric matrix (C) Zero matrix (D) Identity matrix

Choose the correct answer in the Exercises 11 and 12.

Q11.    If A, B are symmetric matrices of same order, then AB – BA is a

            (A) Skew symmetric matrix
            (B) Symmetric matrix
            (C) Zero matrix
            (D) Identity matrix

Answers (1)

best_answer

  If A, B are symmetric matrices then 

                                                 A'=A       and      B' = B

we have,             \left ( AB-BA \right )'=\left ( AB \right )'-\left ( BA \right )'=B'A'-A'B'

                                                                                             =BA-AB

                                                                                             = -(AB-BA)

                       Hence, we have  (AB-BA) = -(AB-BA)'

Thus,( AB-BA)' is skew symmetric.

Option A is correct.

     

Posted by

seema garhwal

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