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Question
If A, B are symmetric matrices of same order, then AB − BA is a ______.
Options
Skew symmetric matrix
Symmetric matrix
Zero matrix
Identity matrix
Solution
If A, B are symmetric matrices of same order, then AB − BA is a Skew symmetric matrix.
Explanation:
We know that A' = A, B' = B
So, (AB - BA)' = (AB)' - (BA)'
= B'A' - A'B' = BA - AB
= -(AB - BA)
AB - BA is a skew-symmetric matrix.
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