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Suppose A an nxn matrix has all real values and it is also skew symmetric (A^T =...

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Suppose A an nxn matrix has all real values and it is also skew symmetric

(A^T = - A) then which of the following is/are true?

I. if n is odd then det(A) = 0

II. A is always diagonalizable

III. if n is even then det(A) = 0

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