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Question

Show that the elements on the main diagonal of a skew-symmetric matrix are all zero.

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Solution

Let A=[aij] be a skew-symmetric matrix. Then,

aij=aji for all i, j.

aii=aii for all values of i.

2aii=0

aii=0 for all values of i.

a11=a22=a33=...=ann=0.

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