Let A = [aij] be a skew - symmetric matrix Then aij = - aji for all i , j , ⇒ aij = - aij for all values of i = j ⇒ 2aii = 0 ⇒ aii 0 for all i Now, let A be any square matrix then
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(A+A′) =
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[A′+(A′)] [Since (A + B) = A' + B' ] =
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(A' + A) [since (A')' = A] ⇒
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(A + A') is symmetric matrix Also
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(A - A')' =
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[A' - (A')'] =
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(A' - A) = −
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(A - A') ⇒
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(A - A') is skew - symmetric matrix. Hence option [a] is correct