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Skew Symmetric Matrix

A skew symmet...

Question

A skew symmetric matrix $S$ satisfies the relation $S^{2} + I = 0$ , where $I$ is a unit matrix, then $S S^{'}$ is equal to

I

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2 I

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- I

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None of these

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Solution

The correct option is B $I$
$S^{2} + I = 0 ⟶ (a)$
S is skew symmetric mtrix
So,
$S^{'} = - S ⟶ (b)$
Using equation (a),
$I = - S^{2} I = - S S (- S = S^{'}) I = S^{'} S$

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