Let 8: MnXn (F) * F be an n-linear function and F a field that does not have

Chapter 4, Problem 19

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Let 8: MnXn (F) * F be an n-linear function and F a field that does not have characteristic two. Prove that if 8(B) = 8(A) whenever B is obtained from A G MnXn (F) by interchanging any two rows of A, then 8(M) = 0 whenever M G MnXn (F) has two identical rows.

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