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Question 1062855: show that the product of two skew symmetric matrices is diagonal.Is this true for n x n skew symmetric matrices with n>2 or n=2 ?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Recall that A is a skew symmetric matrix implies that A^T = -A, also the diagonal of A is zeroes
if A = (a(i,j)) then the elements are written a(i,j) = -a(j,i)
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A is the sum of its symmetric and skew symmetric components, namely
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A = ((A + A^T)/2) + ((A - A^T)/2)
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Note that a diagonal matrix has all off-diagonal elements equal to zero
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Let A and B be skew symmetric matrices, then their product AB is symmetric
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AB = (AB)^T
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This is only true for n = 2, then we have AB is diagonal and symetric
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