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If A and 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
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If A and B are symmetric matrices of same order, then AB – BA is...
A and B are symmetric matrices.
⇒ A = A’ and B = B’
Now, (AB – BA)’ = (AB)’ – (BA)’ ...(i)
⇒ (AB – BA)’=B’A’ – A’B’ [By reversal law]
⇒ (AB – BA)’ = BA – AB [From Eq. (i)]
⇒ (AB – BA)’ = –(AB – BA)
⇒ (AB – BA) is a skew-symmetric matrix.
⇒ A = A’ and B = B’
Now, (AB – BA)’ = (AB)’ – (BA)’ ...(i)
⇒ (AB – BA)’=B’A’ – A’B’ [By reversal law]
⇒ (AB – BA)’ = BA – AB [From Eq. (i)]
⇒ (AB – BA)’ = –(AB – BA)
⇒ (AB – BA) is a skew-symmetric matrix.
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If A and B are symmetric matrices of same order, then AB – BA is a:a)Skew-symmetric matrixb)Symmetric matrixc)Zero matrixd)Identity matrixCorrect answer is option 'A'. Can you explain this answer?
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