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Question
If A and B are matrices of same order, then (AB′ – BA′) is a ______.
Options
Skew-symmetric matrix
Null matrix
Symmetric matrix
Unit matrix
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Solution
If A and B are matrices of same order, then (AB′ – BA′) is a skew-symmetric matrix.
Explanation:
Let P = (AB' – BA')
P' = (AB' – BA')'
= (AB')' – (BA')'
= (B')A' – (A')'B' ......[∵ (AB)' = B'A']
= BA' – AB'
= – (AB' – BA')
= – P
P' = – P
So it is a skew symmetric matrix.
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