(B) For any skew-symmetric matrix $A$ of order $n$,we have $A^T = -A$.Taking the determinant on both sides,we get $|A^T| = |-A|$.Since $|A^T| = |A|$ a

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(B) For any skew-symmetric matrix $A$ of order $n$,we have $A^T = -A$.Taking the determinant on both sides,we get $|A^T| = |-A|$.Since $|A^T| = |A|$ and $|-A| = (-1)^n |A|$,we have $|A| = (-1)^n |A|$.For a $3 \times 3$ matrix,$n = 3$,so $|A| = (-1)^3 |A| = -|A|$.This implies $2|A| = 0$,which means $|A| = 0$.

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

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If $A$ is a $3 \times 3$ order skew-symmetric matrix,then $|A|$ is equal to:

GSEB 2015 All GSEB

A
$1$
B
$0$
C
$-1$
D
$3$

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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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If $A$ is a $3 \times 3$ order skew-symmetric matrix,then $|A|$ is equal to:

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