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If $A$ is a $3 x 3$ skew-symmetric matrix with real entries and trace of $A^{2}$ equals zero, then

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A=O

2A=I

A is orthogonal

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Correct option is A

Let A=a b cb d ec e fTrace of A2=a2+b2+c2+b2+d2+e2+c2+e2+f2⇒a2+2b2+2c2+d2+2e2+f2=0As a, b, c, d, e, f are real numbers, we get a=b=c=d=e=f=0.∴A=0

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If A is a 3x3 skew-symmetric matrix with real entries and trace of A2 equals zero, then

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If $A$ is a $3 x 3$ skew-symmetric matrix with real entries and trace of $A^{2}$ equals zero, then