Which one of the following statements is corr | vedclass

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(B) Let $A$ be a skew-symmetric matrix of order $n 	imes n$. By definition,$A^T = -A$. Taking the determinant on both sides,we have $\det(A^T) = \det

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Skew-symmetric matrix of odd order is singular

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(B) Let $A$ be a skew-symmetric matrix of order $n 	imes n$. By definition,$A^T = -A$. Taking the determinant on both sides,we have $\det(A^T) = \det(-A)$. Since $\det(A^T) = \det(A)$ and $\det(-A) = (-1)^n \det(A)$,we get $\det(A) = (-1)^n \det(A)$. If $n$ is odd,then $(-1)^n = -1$,so $\det(A) = -\det(A)$,which implies $2 \det(A) = 0$,or $\det(A) = 0$. $A$ matrix with a determinant of $0$ is called a singular matrix. Therefore,a skew-symmetric matrix of odd order is always singular.

Which one of the following statements is correct regarding skew-symmetric matrices?

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