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## Homework Statement

I am to show that the trace of the product of a symmetric and a skew-symmetric matrix is zero.Please check what I did is corect:

## Homework Equations

## The Attempt at a Solution

Let me assume:A~=A and B~=-B

(I will use # sign to denote the sum process)

trace(AB)=[#(i)](AB)_ii=[#(i)] [#(j)] a_ij*b_ji

trace(AB)=-[#(j)] [#(i)] b_ji*a_ij using conditions on A and B

=-[#(j)](AB)_jj

Since i and j are equivalent,

what we have is 2trace(AB)=0

hence,conclusion