How do I prove that an anti-symmetric matrix $A$ is not invertible? [duplicate]

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$A$ is a square anti symmetric matrix with dimension $n\times n$.

It is known that $n$ is an odd number. Prove that $A$ is not invertible.

How do I prove this? any hints please?

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1 Answer

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$$\det(A)=\det(A^T)=\det(-A)=(-1)^n\det(A)=-\det(A)$$ since $n$ is odd. hence $$\det(A)=0$$

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