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Question
Sum of two skew-symmetric matrices is always ______ matrix.
Solution
Sum of two skew-symmetric matrices is always skew-symmetric matrix.
Explanation:
Let A and B be any two matrices
∴ For skew-symmetric matrices
A = –A' ......(i)
And B = –B' ......(ii)
Adding (i) and (ii) we get
A + B = –A' – B'
⇒ A + B = –(A' + B')
So A + B is skew-symmetric matrix.
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