(A) Let $A$ be a skew-symmetric matrix of odd order $n$,where $n = 2k + 1$ for some integer $k \ge 0$.Since $A$ is skew-symmetric,we have $A^T = -A$.T

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(A) Let $A$ be a skew-symmetric matrix of odd order $n$,where $n = 2k + 1$ for some integer $k \ge 0$.Since $A$ is skew-symmetric,we have $A^T = -A$.Taking the determinant on both sides,we get $|A^T| = |-A|$.Using the property $|A^T| = |A|$ and $|cA| = c^n|A|$ for a matrix of order $n$,we have:$|A| = (-1)^n |A|$.Since $n$ is odd,$(-1)^n = -1$.Therefore,$|A| = -|A|$.$2|A| = 0 \Rightarrow |A| = 0$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Special types of matrices, Transpose of matrices and Trace of matrices

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Let $A$ be a skew-symmetric matrix of odd order,then $|A|$ is equal to

A
$0$
B
$1$
C
$-1$
D
None of these

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3 and 4 .Determinants and Matrices

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Special types of matrices, Transpose of matrices and Trace of matrices

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Let $A$ be a skew-symmetric matrix of odd order,then $|A|$ is equal to

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If $A$ is a skew-symmetric matrix,then (given $n \in N$):
$1$. $A^{2n}$ is a skew-symmetric matrix.
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