If $A$ is a $3 imes 3$ skew-symmetric matrix, then trace of $A$ is equal to

Question

If $A$ is a $3 	imes 3$ skew-symmetric matrix, then trace of $A$ is equal to

Dr. Abubacker · Accepted Answer

(c)
As A is a skew-symmetric matrix,
$A^{T} = - A$
$\Rightarrow a_{ij} = 0,\ \forall\ \ i$
$\Rightarrow$tr($A$)$= 0$
Also,
$|A| = \left| A^{T} \right| = | - A| = ( - 1)^{3}|A|$
$\Rightarrow 2|A| = 0$
$\Rightarrow |A| = 0$

Q. If $A$ is a $3 \times 3$ skew-symmetric matrix, then trace of $A$ is equal to

Explanation

Reviewed by Dr. Abubacker

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